Pitts was born in Sheffield, England. His family was working-class, his parents being a joiner . working as a car mechanic in his early career. And wrote a letter to the college to get out of college classes to become an actor. His family were livid at this. During his time at Stannington College, Sheffield Barry Hines paid a visit looking for extras for his upcoming drama Looks and Smiles. Pitts was cast and soon upgraded to a bigger role in the production. He decided to follow his ambition to become an actor in 1983.

In 1983, Pitts was landed in the role of loveable young rogue Archie Brooks in the British soap opera Emmerdale. Pitts was chosen for the role by Kevin Laffan, who watched Pitts portray the title character in a theatrical adaptation of Nicholas Nickleby, and believed that Pitts’ versatile acting ability and his strong Yorkshire accent, meant he was well suited for the role. The role was Pitts’ very first role in a television series, and he first appeared on the show on 18 November 1983, and remained in the show for a total of ten years, involved in storylines that included his prison sentence in 1989 for setting fire to Seth Armstrong’s property, becoming a suspect of whether or not he was the father of Elsa Feldmann’s child in 1990, and his relationship with lesbian Zoe Tate in 1993.

In 1993, Pitts was axed from the show, and Archie was killed off in the infamous Emmerdale plane crash. He made his last appearance on the show on 30 December 1993.

During his time away from Emmerdale, Pitts had notable guest appearances in shows including Casualty as Aidan Phillips in 1996, EastEnders as Cliff in 1996, The Bill as Chris Riley in 1999, The Royal as Alec Glazer in 2004 and Unforgiven in 2009 as Adam Boothroyd. Tony was the original choice for Terry Duckworth in Coronation Street, but Nigel Pivaro ended up playing the role instead. Pitts starred in Lilyhammer as Danny Croc Hammer, the brother of Duncan Hammer.

Pitts has appeared in the police drama Heartbeat on two occasions, the first time in 1998 as Carl Southall and the second time in 2005 as Brian Gilbert. In 2002, he appeared as DI Healey in the miniseries In Deep alongside Nick Berry and Stephen Tompkinson.

Pitts is currently appearing in Scott & Bailey on ITV1/ITV1HD as Adrian Scott (the husband of Lesley Sharp’s character, DC Janet Scott). Pitts also had a small role in the 2012 film War Horse. In 2012 Pitts starred in the third episode of Dirk Gently as Robbie Glover. In 2012 he also appeared as the Chief Superintendent in the Sherlock episode “The Reichenbach Falls”. In 2013 he appeared as Sergeant Moss in the BBC drama series Peaky Blinders. Pitts played ‘Captain Patero’ in ‘Rogue One: A Star Wars Story’ in 2016. He also appeared as Detective Chief Superintendent Les Hargreaves in the 2014 second series of BBC’s Line of Duty, made an appearance in the series finale of series four in 2017, and then appeared in series five in 2019. Pitts is also appearing in Wild Bill on ITV in 2019.