Tony Cohen was born on 4 June 1957 and grew up in Melbourne. His father was Jewish and his mother was an Australian of Irish descent. In 1975 Cohen began working as a sound Engineer. In April of the following year he was working at Armstrong Studios with Molly Meldrum, media personality and some-time Producer, on Perth's glam-rock group, Supernaut's lead single, "I Like It Both Ways". Cohen produced the group's associated self-titled album and its follow-up single, "Too Hot to Touch".

In July 1976 Cohen and fellow Engineer, Ian MacKenzie, met with Meldrum to organise the production of The Ferrets' debut album, Dreams of a Love: "It was all a bit of Elton John, a bit of the 'Real Thing', [Meldrum] called us in for a production meeting 9:00 in the morning at his place and he was still in bed [...] and putting the music on [...] very, very loud and then proceeds to shout at you over the top of it, and we were all sitting there sort of terrified thinking, what on earth is he saying?" After a year production was incomplete so The Ferrets took over, together with Cohen and MacKenzie; it was finalised in August 1977 and released in October.

In June 1978 Cohen started working with The Boys Next Door (later known as The Birthday Party), as Engineer at Richmond Recorders on their debut album, Door, Door (1979), then their early EP, Hee Haw (December 1979) and, as engineer-producer, on their second album, The Birthday Party (November 1980). The group's leader, Nick Cave, used Cohen as Engineer or Producer for almost two decades with his next group, Nick Cave and the Bad Seeds, from From Her to Eternity (18 June 1984) to No More Shall We Part (2 April 2001).

The Cruel Sea used Cohen's services for their debut studio album, This Is not the Way Home (December 1991). He was nominated at ARIA Music Awards of 1993 for Producer of the Year for that album and for "Get Thee to a Nunnery", a track on TISM's EP, The Beasts of Suburban (20 July 1992). At the following year's ceremony Cohen won Producer of the Year for The Cruel Sea's next album, The Honeymoon Is Over (May 1993). In 1995 he won both Engineer of the Year and Producer of the Year. Over the previous 18 months – the eligibility period – Cohen had produced Let Love In (Nick Cave and the Bad Seeds, 18 April 1994), You Wanna Be There But You Don't Wanna Travel (Dave Graney 'n' the Coral Snakes, June 1994), Parables for Wooden Ears (Powderfinger, 18 July 1994), Livin' Lazy (Maurice Frawley and Working Class Ringos, 1994), Three Legged Dog (The Cruel Sea, April 1995), Kim Salmon and the Surrealists (Kim Salmon and the Surrealists, April 1995) and Mouth to Mouth (The Blackeyed Susans, July 1995).

~Mixed Relations' "Love" 1993 "Take it or Leave It" 1992

After the year 2000 Cohen's name started appearing less regularly on album credits and he had effectively retired, but he emerged in 2017 to produce Augie March's album Bootikins, as he had always wanted to work with the group. He died unexpectedly before the album's sessions concluded, and Augie March leader Glenn Richards stated "It still amazes me that we got a chance to work with the man. The moments are ours and we will cherish them ... He got us feeling like and playing like a real band again after a long interim, and we made some very good music together.".

Cohen reflected on his early work with Cave, in an interview with Richard Fidler in September 2006, "[it] was all very experimental then, because we were all learning – I fell in love with this new way of recording... because there were no rules. We were looking for sounds that made your fillings drop out rather than pleasant pop tunes, so we got to do crazy things like find concrete stairwells and abuse equipment, so it was all very attractive for me. Some of it didn't work, but as history has shown Nick really honed his craft, he's done some brilliant records... some of the early stuff was a bit rough but it was a learning curve then." Ed Nimmervoll, an Australian Journalist and Editor of Rock Australia Magazine, recalled "Nick Cave's Birthday Party were allowed to take up some of the studio time slack. Rather than home, their Producer Tony Cohen slept in the air conditioning duct."