The match will see Stuart Pearce's side pitted against one of the favourites for the competition. It will be part of a double-header at the Riverside Stadium with Team GB women's team, coached by Hope Powell, taking on Sweden before the men play Brazil.
A Great Britain team last played an international in an Olympic qualifier against Bulgaria in 1971, and have not played in an actual Games since 1960.
Pearce said: "I've learned a great deal about the Olympics since I was given the opportunity to lead this team and I realise just how massive an event it is going to be for the whole of Great Britain.
"In world football they don't come much bigger than Brazil and it should be a terrific occasion for us going into our first match. I think particularly with the Brazilian connections on Teesside it will be a terrific turnout again come July."
Team GB women are competing at their first Olympics and Powell said: "Sweden are a strong side and we want that challenge to be ready for 25 July when the Olympics begins for us.
"It is a huge opportunity, both in this country and worldwide, to showcase women's football to a bigger audience and grow the game."
It is the first men's and women's international double-header since 1989 when England women played Sweden, and Bobby Robson's England took on Chile at Wembley.