The indoor complex in Middlehaven will include a 557ft (170m) ski slope, climbing area, indoor sky-diving centre, shops and cafes.
Developer Cool Runnings (NE) expect the centre to attract 2.5m visitors a year.
Building work is expected to start early next year, with a forecast opening by the summer of 2019.
Middlesbrough Council described the scheme as a "massive step" in the town's regeneration plans.
Paul Mosley, of Cool Runnings NE, said: "This is fantastic news for us as developer and for Middlesbrough as a whole.
"The feedback we have had from local people has been superb. People have been screaming out for something like this in Middlesbrough.
"There is already a lot of development in Middlehaven and this will just be the icing on the cake."
The project is the latest phase in the regeneration of Middlehaven, with more than £150m already being spent on housing, leisure and business developments.
The nearest snow centre to Middlesbrough is currently in Castleford, West Yorkshire.
Plans for a £30m snow and leisure centre, which is expected to create more than 300 jobs, have been approved by councillors in Middlesbrough.