Dragonetti was born in Venice, Italy, of Pietro Dragonetti, a barber and amateur musician, and Caterina Calegari. He began playing the guitar and the double bass by himself on his father's instruments. He was soon noticed by Doretti, a violinist and composer of ball music, who took him along for public performance in Venice. At the age of twelve, he was placed under the tuition of Berini, the best master for the double bass in Venice, who decided after only eleven lessons that he could not teach the boy anything more. At the age of thirteen, Dragonetti was appointed principal player at the Opera Buffa in Venice. At fourteen he was appointed principal double bass player in the Grand Opera Seria at the San Benedetto theatre.

When about eighteen, in Treviso, he was invited to join the quartet of Tommasini, and was noticed by Morosini, procurator of San Marco, who indulged him in auditioning for the admission in the Chapel of San Marco. He made a first attempt in 1784, which was lost to Antonio Spinelli. He finally joined the institution on September 13, 1787 as the last of the five double bass players of the Chapel with a yearly income of 25 ducats. He soon became the principal bassist. He later was offered a place by the Tsar of Russia, which was declined and got him a salary raise in the Chapel. He became very famous at the time, started playing solo pieces, which was exceptional at the time for the double bass, and even got elected as one of the directors of a musical festival held for the coming of fourteen sovereign princes to the republic of Venice. One of his concertos was particularly remarked by the queen of Naples.

When in Vicenza for an engagement at the Grand Opera there, he acquired his famous Gasparo da Salò double bass from the Benedictine Nuns of the Convent of San Pietro (La Pieta) in Vicenza, which is now housed in the museum of St Mark's Basilica. He was offered another position to the Tsar of Russia, which he declined after the procurators of St Mark increased his salary to an exceptional 50 ducats. They even granted him a leave for a year, with a continuation in his wages, to go to the King's Theatre in London. That leave was extended for three more years afterwards, but finally Dragonetti never returned to Venice for more than a brief period during the French occupation of the city, 1805 - 1814.

Dragonetti had no close family, but had many close friends in the musical world in London. The story that he kept and often traveled with a collection of life-sized cloth mannequins, bringing them to his concerts and having them placed in front row seats of theaters, and even introducing one of these dolls as his wife, is completely unsubstantiated. He was an avid collector, and did indeed collect dolls, sometimes taking one along on trips to amuse the children, of whom he was very fond. He never did learn to speak English, expressing himself in a mixture of Italian, English, French and the Venetian dialect, but was an astute businessman, and in fact, helped his surviving family in Venice financially.

He left Venice on September 16, 1794, partly under the influence of his friend, Giovanni Battista Cimador, and participated in the first rehearsals at the King's Theatre, on October 20, 1794, and finally appeared as orchestra member in the opera Zenobia in Palmira, by Giovanni Paisiello, on December 20, 1794. After only a few months, he became very famous in London, and his brilliant career was to last till the end.

Later he became intimate with the Prince Consort and the Duke of Leinster. He took part between 1816 and 1842, in forty-six concerts held by the Philharmonic Society of London. At the Italian Opera orchestra, he met the cellist Robert Lindley, who became his close friend and with whom he shared the stand during fifty-two years. They made a specialty at playing Arcangelo Corelli's sonatas.

He died in his Leicester square lodgings at the age of 83, and was buried on April 23, 1846 in the vaults of the Roman Catholic chapel of St Mary, Moorfields, and was moved in 1889 to the Roman Catholic cemetery at Wembley. Vincent Novello and Count Carlo Pepoli (librettist of Vincenzo Bellini's I puritani) were among his most famous friends in London.

In 1791 - 1792, Joseph Haydn accepted a lucrative offer from German impresario Johann Peter Salomon to visit England and conduct new symphonies with large orchestras. The visit was a huge success and generated some of his best known work. Another trip was therefore scheduled in 1794 - 1795. On that second occasion, Haydn met Dragonetti, who became a very good friend, and who visited him in Vienna in 1799. On that first trip to Vienna, Dragonetti also met Beethoven in a famous encounter.

"Two new and valuable, though but passing acquaintances were made by Beethoven this year, however - with Domenico Dragonetti, the greatest contrabassist known to history, and Johann Baptist Cramer, one of the greatest pianists. Dragonetti was not more remarkable for his astounding execution than for the deep, genuine musical feeling which elevated and ennobled it. He was now - in the spring of 1799, so far as the means are at hand of determining the time - returning to London from a visit to his native city, Venice, and his route took him to Vienna, where he remained several weeks. Beethoven and he soon met and they were mutually pleased with each other. Many years afterwards Dragonetti related the following anecdote to Samuel Appleby, Esq., of Brighton, England: "Beethoven had been told that his new friend could execute violoncello music upon his huge instrument and one morning, when Dragonetti called at his room, he expressed the desire to hear a sonata. The contrabass was sent for, and the Sonata, n°2, of Op.5, was selected. Beethoven played his part, with his eyes immovably fixed upon his companion, and, in the finale, where the arpeggios occur, was so delighted and excited that at the close he sprang up and threw his arms around both player and instrument". The unlucky contrabassists of orchestras had frequent occasions during the next few years to know that this new revelation of the powers and possibilities of their instrument to Beethoven was not forgotten." (Alexander Wheelock Thayer, 1967)

To this day, the mastering of the Beethoven double bass symphonic parts are considered a basic standard for all orchestral double bass players. Dragonetti came back to Vienna for an extensive stay in 1808 - 1809. On that second trip he became friends with composer Simon Sechter, who would become the court organist in 1824, and professor of composition at the Vienna Conservatorium in 1851. He wrote piano accompaniments to some of his concert pieces, and they maintained a lifelong correspondence. Dragonetti was again in Vienna in 1813 and got to meet once more Beethoven, who had just written Wellington's Victory, to celebrate the victory of Wellington over the French armies of King Joseph Bonaparte at the Battle of Vitoria. The premiere of this work, as well as of Beethoven's seventh symphony was performed on December 8, 1813, in the University's Festsaal, with Dragonetti leading the double basses.

Dragonetti was known for his formidable strength and stamina. It was particularly important at a time when the role of the double bass in the orchestra was to assist the concertmaster in maintaining the cohesion and establishing the tempo. He had a huge hand, with strong, broad fingers, which allowed him to play with a taller bridge and strings twice as far from the fingerboard as the other bassists.

The physical quality is his huge hand: endowed, first of all, with prodigious strength so that its grip on the strings of the instrument is the equivalent of the grip of a blacksmith's vice... A hand endowed with five fingers so long, big and agile, that all five, including the bent thumb, go up and down the fingerboard each playing a note. (Caffi, 1855)

This was not at all standard in these times, as most players used to play - in one position - one note with the index finger, and one with the other three fingers in combination.

Dragonetti was a lover of the fine arts, and a collector of musical instruments as well as many art-related articles, such as original scores and paintings. When he died, the following instruments were dispatched: a giant double bass attributed to Gasparo da Salò and stated to have been used in contemporary performances of Handel's music, which is now conserved in the Victoria and Albert Museum in London; a very fine Domenico Montagnana Basso di Camara (from Venice); a Gasparo da Salò double bass dated 1590; an Amati double bass; a Maggini double bass; a Stradivarius violin (once played by Paganini), now known as the "Dragonetti"; a Gasparo da Salò violin; two Amati violins; one Lafont violin; a Stradivarius violin copy; 26 unnamed violins; a Gasparo da Salò viola; an Amati viola; a Hill viola; 5 unnamed violas; 6 cellos; a large cello; 3 guitars; 2 bassoons; 3 French horns.

"There are various stories of how Dragonetti came into possession of the famous Gasparo da Salo bass. The fascinating and highly commendable biography Domenico Dragonetti In England by Fiona M. Palmer (Clarendon Press Oxford 1997) seems to offer the most plausible account. Because of Dragonetti's unprecedented virtuosity as a soloist, attractive offers of work were made from both London and Moscow. As remuneration for renouncing the offers and remaining as principal bassist with the orchestra of the Ducal Chapel of St Mark's in Venice (an orchestra of considerable importance), a decree made in 1791 gave Dragonetti a financial gratuity. Similarly, it is reputed that Dragonetti was presented with an instrument made by Gasparo da Salo (1542 – 1609) by the Benedictine nuns who occupied St Peter's monastery in Vicenza where Dragonetti lived and played in the Grand Opera. In the Palmer biography, a footnote refers to a 1906 account by C.P.A. Berenzi, who suggests that the instrument may have been made for the monks of St Peter's, Vicenza, by Gasparo da Salo, and acquired by the procurators of St Mark's to entice Dragonetti to remain in their employ.

When he left for London in 1795, Dragonetti left many papers and manuscripts, including a Complete system of the double bass, or instruction book for that instrument, containing many elaborate exercises and studies, in the care of a friend. Unfortunately, they were sold and could not be retrieved by their author when he returned to Venice after some years. Today, many of his letters, personal papers, compositions, solos and manuscripts are to be found in the British Library. Some were directly bequeathed by Dragonetti, some were offered by Vincent Novello, and some were bought at auctions.