Inghelbrecht was born in Paris, the son of a viola player. He studied at the Paris Conservatoire and made his debut as a conductor in 1908 at the Théâtre des Arts.

Inghelbrecht entered the Conservatoire aged 7 and studied solfege, harmony and violin. At the aged of 16 he was expelled when caught playing the violin in local cafes. Around this time he was appointed second violin at the Concerts de l'Opéra; his friend Pierre Monteux, then conductor of the Concerts Berlioz, would use him as a substitute – all of which gave him important experience.

In 1908 he conducted the first performance of Florent Schmitt's La tragédie de Salomé which was a success and led to more engagements with leading musicians, including acting as chorus master for the first performance of Claude Debussy's Le martyre de Saint Sébastien. In 1913 he was appointed as director of the new Théâtre des Champs - Élysées, inaugurated on 2 April. In 1919 Inghelbrecht conducted the first performance of André Caplet's arrangement of Debussy's La Boite a joujoux; he also founded the Concerts Pleyel devoted to music of the 16th to 18th centuries. In 1921 he conducted the premiere of Les mariés de la tour Eiffel, a ballet by five of the members of Les six.

Inghelbrecht was music director of the Opéra - Comique in 1924 - 25, where he conducted Manon, a new production of Tristan und Isolde, Pelléas et Mélisande, Masques et bergamasques, and Pénélope; he also conducted several ballets including the premiere of his own Jeux de Couleurs. From 1928 to 1932, he conducted the Concerts Pasdeloup and briefly held the directorship of the Opera d’Alger in 1929.

In 1934 Inghelbrecht was asked to form a national radio orchestra – to become the Orchestre National de la Radiodiffusion Française (ONF). The following year he fulfilled a long held ambition to conduct the first Paris performance of the 1874 edition of Boris Godunov.

During the 2nd World War, the ONF was evacuated to Rennes, then Marseilles and returned to Paris in 1943. However when planning the 1,000thperformance of the orchestra (and commemorating the 25th anniversary of the death of Debussy), Inghelbrecht refused to conduct a program of the occupying forces and on 18 July 1943 received a note suspending his appointment by order of President Laval.

From 1945 to 1950 Inghelbrecht was conductor of the Paris Opéra, and returned to the ONF in 1947. From 1958 to 1965 he devised weekly radio programs called 'Entretiens autour d’un piano'.

Both in his conducting career and writing he championed Debussy, Ravel, Roussel, Chabrier and Schmitt.

He corresponded with Debussy - a close friend - from 1911 until Debussy's death in 1918. He was a member of Les Apaches along with Ravel, Schmitt and others.

He was married three times: to Colette Steinlen (1910, divorced in 1920), Carina Ari (1928), and Germaine Perrin. With the latter he wrote a biography of Debussy in 1953.

Although self - taught as a composer, Inghelbrecht left around 60 compositions. The style of his compositions is eclectic. Even when stylistically unoriginal, his polished, masterly orchestration makes his work worthy of closer attention. The operetta Leïla (or Virage sur l’aile) of 1947, is a hilarious comedy and eminently singable entertainment. The opera - ballet Le chêne et le tilleul (after La Fontaine) of 1960 is the climax of the composer’s output with harmonies in the style of Debussy contrasting with the Bacchic frenzy of wild dances with pungently rhythmic, virile accompaniment. La Nursery for piano four - hands consists of 36 short pieces composed between 1905 and 1932 and some later orchestrated.