The scheme at the Etihad Campus close to Manchester City’s ground won the backing of the council’s planning committee during a meeting on Thursday.
It will form part of the £300m entertainment zone called Medlock Square near to the Co-op Live arena.
Plans for the new venue were submitted earlier this year.
Questions were asked during the council meeting about its impact on the roads and local area when events are taking place at the Etihad Stadium, Co-op Live, and new theatre venue at the same time.
It is thought there will be around 15 arena and match days taking place over the year.
A council officer said the “reality is when you have a huge facility like this close to the city centre, the impetus will always be to ensure that as many people as possible get there by public transport or active forms of transport, that’s the objective of the strategy that we have for the campus”.