The son of a head postmaster, Peebles attended Bishop's Stortford College, Hertfordshire before training in hotel management at Bournemouth College Of Technology. After DJing at a college dance he was offered a job at Samantha's in Bournemouth. He worked at Chelsea Village, The Scotch of St. James in London and at the Hardrock in Manchester.
He began his broadcasting career in 1973, presenting a Saturday morning show for BBC Radio Manchester. In 1974, Peebles helped launch Manchester's Piccadilly Radio where he first broadcast Andy Peebles' Soul Train, before joining BBC Radio 1 in 1978, where he presented the Monday-Thursday evening show from 8-10pm.
In September 1979, Peebles briefly presented weekday afternoons, taking over from Tony Blackburn, before moving to a 10.30am-12.30pm weekday show.
Peebles' name was thrust into the media spotlight in December 1980 when John Lennon was murdered in New York. He had conducted the last British media interview with Lennon at the Hit Factory recording studio, two days before Lennon's death. The Lennon interview was later published in print as The Lennon Tapes, now in print as The Last Lennon Tapes.
In 1981, Peebles began to present a regular Friday evening show, mixing music and sport, and in 1983, he started a weekly show entitled My Top 10, where he would interview stars from music, the arts and sport.
In 1987, he presented Andy Peebles' Soul Train for Radio One, firstly on Sunday nights from 9-11pm and then in 1989, on Saturday evenings.
In September 1990, Peebles moved to the 12-2am slot on Friday night/Saturday morning, and in May 1991 he was heard from 12-4am as Radio 1 started broadcasting 24 hours a day
During 13 years at Radio One he also broadcast for BBC World Service, BBC Schools Radio, BFBS Radio & BBC Radio London/GLR.
Peebles left Radio 1 in March 1992. He then joined BBC Radio Lancashire to present the morning show before hosting the Late Show for BBC North. He has presented shows on BBC Radio 5 and both reported and commentated on cricket for BBC Network and Local Radio for 27 seasons.
Peebles joined BBC Radio 2 from 1999–2002, where he presented his Soul Show on Wednesday evenings. He then joined Jazz FM in both London and the North West of England presenting a Saturday afternoon mix of sport and soul music. He took over the evening show when Smooth Radio went national & presented the show until January 2013. Andy Peebles' Soul Train was heard every Saturday from 8.00pm until midnight featuring The Quiet Storm. The last edition was broadcast on 28 September 2013. Andy joined Gold on 2 November 2013 to present Andy Peebles' Soul Train and the series ran until 22 March 2014. On 5 April 2014 the programme celebrated 40 years on the air having first been broadcast on Piccadilly Radio, Manchester on Friday April 5, 1974.
In November 2011 he was elected to The Radio Academy Hall of Fame.
He went on tour around the UK from September 2013 with a one man show "The Perfect Face For Radio" celebrating four decades of broadcasting and taking an affectionate look back at his career.