BAM has already been carrying out preliminary works but an official ground breaking ceremony was held this week to mark the start of work.
BAM has been developing the design from Glasgow-based architect Page/Park.
The two theatres forming the Playhouse opened originally in 1990 and at the time they were the largest purpose-built new theatres in the UK since the National Theatre in 1976. However, disabled access is poor and they require new entrances, with more open spaces.
The scheme is part of a wider transformation of the local Quarry Hill area as a cultural quarter.
BAM construction director Jason Pink said: “We’re creating a new theatre in the undercroft and we’ll be conducting enhancement and access works around the other two existing theatres.
“It’s a complex refurb with numerous small spaces that feel like a rabbit warren. Our team has experience of similar restoration schemes that we completed in Leeds and Harrogate.”
BAM’s track record on leisure schemes in Yorkshire includes the Leeds First Direct Arena, the Cargenie Pavilion at Headingley and the Melrose Stand at York Racecourse. It was also behind the restorations of City Varieties Musical Hall, the Royal Hall in Harrogate, and Sheffield City Hall.