The complex in Giffnock will provide an eight-lane swimming pool, fitness suite and a four-court games hall.
The theatre will include a 364-seat auditorium and stage, a smaller studio theatre, dressing rooms and bar and lounge areas.
Previous plans had been approved in 2022 but the council later decided to scale back the project after construction inflation pushed the price to £67m.
The new £56m facility will be built alongside the existing leisure centre in Eastwood Park.
Construction of the new complex is due to begin later this year, though some preliminary work will be required before then.
A spokesperson for East Renfrewshire Council said: ‘This is a significant milestone in our plans to replace facilities which are more than 40 years old and no longer fit for purpose.
“The council is committed to delivering a new leisure centre and theatre to provide much-improved amenities for local residents for generations to come.’
The complex is due to open in the second half of 2027 and the existing leisure centre and theatre would then be demolished.