Hope Powell's women's team will play New Zealand in the opening event of the Olympic Games at the Millennium Stadium in Cardiff on 25 July.
They will then face further group games against Cameroon and Brazil.
The Team GB men's side will take on Senegal in their opening fixture, at Old Trafford on 26 July.
Stuart Pearce's side also face United Arab Emirates and Uruguay in the group stage of the men's Olympic football competition.
"Uruguay will be tough but I wouldn't dismiss anyone," said Pearce after the draw.
"The addition of three overage players can contribute to a really strong side. It will be tough, tournament football always is. Everyone in the squad will have star quality but I'll pick the squad on merit.
"The squad may not reflect every home nation and celebrity but they will be the best 18 players who have the best opportunity to deliver a gold. That's my only criteria."
Each team in the men's competition comprises 18 players, with 15 of them born after 1 January 1989.
It means that Liverpool's Luis Suarez could play for Uruguay in the tournament, while Newcastle duo Papiss Cisse and Demba Ba would be eligible to feature for Senegal.
The African side were the last team to qualify for the competition, sealing their place with a play-off victory over Oman at the City of Coventry Stadium on Monday.
There are no restrictions for the women's competition and Powell said she was looking forward to three exciting group fixtures.
"Brazil will be a great game at Wembley, they are always there or thereabouts in major tournaments," said Powell, who is also the coach of the England team.
"Now it is down to our preparations. We have every chance of progressing but we can't take it lightly. We played New Zealand in the World Cup last year and it was a very tough encounter. Cameroon are an unknown quantity.
"This gives us a great opportunity to showcase out sport, we open the Olympics and hopefully we can encourage more females to get into the sport."
The opening ceremony for the Games takes place on 27 July, but both GB teams will have played their first matches by then.
Both Team GB football teams already knew the dates and venues of their opening three fixtures but found out the identity of their opponents at the draw for group stage, which took place at Wembley Stadium, London, on Tuesday.
There are 12 teams in the women's tournament, drawn into three groups of four, while the 16 teams in the men's competition have been split into four groups.
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