Tage Nielsen was educated at the University of Copenhagen, taking his musicological diploma in 1955. He worked for the Music Department of the Danish Broadcasting Corporation in 1951-63, from 1957 as deputy head of the department. He was principal of the Jutland Academy of Music in Aarhus in 1963-83 and Director of the Danish Institute in Rome in 1983-89. He has also held a large number of official posts in Danish musical and cultural life.
His early works, composed at the end of the 1940s and the beginning of the 1950s, are Neoclassically oriented. But from about 1960 he received strong impulses from the musical innovations that came in the 1950s from composers like Stockhausen, Boulez and Nono. This is evident from the works Two Nocturnes for piano (1960), Varianter for alto flute (1963) and Bariolage for orchestra (1965). He was later one of the first Danish composers to make use of quotation elements as formal and expressive devices, for example in the orchestral work Il Giardino Magico (1968). Already here Neoromantic tendencies appeared, and this is a feature that was to characterize many of his works thereafter - for example Three Character Pieces and an Epilogue for piano (1972-74), Three Black Madrigals for a cappella choir (Sylvia Plath) (1978), Passacaglia for orchestra (1981), Paesaggi for two pianos (1985), The Frosty Silence in the Gardens for guitar (1990) and Konzertstück for piano and 11 instruments.
In his opera Laughter in the Dark (after Vladimir Nabokov's novel of the same name) (1986-91) he also makes sophisticated use of quotations and quasi-quotations, among other reasons to create irony and distance in the musicodramatic characterization.
Tage Nielsen was awarded the Ancker Grant in 1975 and Sylvia og Poul Schierbeck's Grant in 1993.