Born in Burslem, Staffordshire, England, the twelfth and last child of Thomas Wedgwood and Mary Wedgwood (née Stringer; d. 1766), Josiah was raised within a family of English Dissenters. He survived a childhood bout of smallpox to serve as an apprentice potter under his eldest brother Thomas Wedgwood IV. Smallpox left Josiah with a permanently weakened knee, which made him unable to work the foot pedal of a potter's wheel. As a result, he concentrated from an early age on designing pottery rather than making it.

In his early twenties, Wedgwood began working with the most renowned English pottery maker of his day, Thomas Whieldon. He began experimenting with a wide variety of pottery techniques, an experimentation that coincided with the burgeoning of the nearby industrial city of Manchester. Inspired, Wedgwood leased the Ivy Works in his home town of Burslem. Over the course of the next decade, his experimentation (and a considerable injection of capital from his marriage to a richly endowed distant cousin) transformed the sleepy artisan works into the first true pottery factory.

Wedgwood married Sarah Wedgwood (1734 – 1815), his third cousin, in January 1764. They had seven children.

Josiah worked in pottery, and his work was of very high quality. If he saw in his workshop an offending vessel that failed to meet with his standards, he would smash it with his stick, exclaiming, "This will not do for Josiah Wedgwood!" He was also keenly interested in the scientific advances of his day and it was this interest that underpinned his adoption of its approach and methods to revolutionize the quality of his pottery. His unique glazes began to distinguish his wares from anything else on the market. He was perhaps the most famous potter of all time.

By 1763, he was receiving orders from the highest levels of the British nobility, including Queen Charlotte. Wedgwood convinced her to let him name the line of pottery she had purchased "Queen's Ware", and trumpeted the royal association in his paperwork and stationery. In 1774, Empress Catherine of Russia ordered the Green Frog Service from Wedgwood; it can still be seen in the Hermitage Museum. An even earlier commission from Catherine was the Husk Service (1770), now on exhibit in Petergof.

As a burgeoning industrialist, Wedgwood was a major backer of the Trent and Mersey Canal dug between the River Trent and River Mersey, during which time he became friends with Erasmus Darwin. Later that decade, his burgeoning business caused him to move from the smaller Ivy Works to the newly built Etruria Works, which would run for 180 years. The factory was so-named after the Etruria district of Italy, where black porcelain dating to Etruscan times was being excavated. Wedgwood found this porcelain inspiring, and his first major commercial success was its duplication with what he called "Black Basalt".

Not long after the new works opened, continuing trouble with his smallpox afflicted knee made necessary the amputation of his right leg. In 1780, his long time business partner Thomas Bentley died, and Wedgwood turned to Darwin for help in running the business. As a result of the close association that grew up between the Wedgwood and Darwin families, Josiah's eldest daughter would later marry Erasmus' son. One of the children of that marriage, Charles Darwin, would also marry a Wedgwood — Emma, Josiah's granddaughter. This double barreled inheritance of Wedgwood's money gave Charles Darwin the leisure time to formulate his theory of evolution.

In the latter part of his life, Wedgwood's obsession was to duplicate the Portland Vase, a blue and white glass vase dating to the first century BC. For three years he worked on the project, eventually producing what he considered a satisfactory copy in 1789.

After passing on his company to his sons, Wedgwood died at home, probably of cancer of the jaw, in 1795. He was buried three days later in the parish church of Stoke-on-Trent. Seven years later a marble memorial tablet commissioned by his sons was installed there.

He belonged to the fourth generation of a family of potters whose traditional occupation continued through another five generations. Wedgwood's company is still a famous name in pottery today (as part of Waterford Wedgwood; see Waterford Crystal), and "Wedgwood China" is the commonly used term for his Jasperware, the blue (or sometimes green) china with overlaid white decoration, still common throughout the world.

He was an active member of the Lunar Society often held at Erasmus Darwin House and is remembered on the Moonstones in Birmingham. He was elected to the Royal Society in 1783 for the development of a pyrometer.

Wedgwood is credited as the inventor of modern marketing, specifically direct mail, money back guarantees, traveling salesmen, self service, free delivery, buy one get one free, and illustrated catalogues.

Wedgwood was a prominent slavery abolitionist. His friendship with Thomas Clarkson – abolitionist campaigner and the first historian of the British abolition movement – aroused his interest in slavery. Wedgwood mass produced cameos depicting the seal for the Society for the Abolition of the Slave Trade and had them widely distributed, which thereby became a popular and celebrated image. The Wedgwood medallion was the most famous image of a black person in all of 18th-century art. The actual design of the cameo was probably done by either William Hackwood or Henry Webber who were modellers in his Stoke-on-Trent factory. From 1787 until his death in 1795, Wedgwood actively participated in the abolition of Slavery cause, and his Slave Medallion, which brought the attention of the public to the horrors of the Slave trade, was very effective in bringing public attention to abolition. Wedgwood reproduced the design in a cameo with the black figure against a white background and donated hundreds of these to the Society for distribution. Thomas Clarkson wrote; "ladies wore them in bracelets, and others had them fitted up in an ornamental manner as pins for their hair. At length the taste for wearing them became general, and thus fashion, which usually confines itself to worthless things, was seen for once in the honourable office of promoting the cause of justice, humanity and freedom".

The design on the medallion became popular and was used elsewhere: large scale copies were painted to hang on walls and it was used on clay tobacco pipes.

A locomotive was named after Josiah Wedgwood and ran on the Churnet Valley Railway.