Wawrinka, the world number 26, won doubles gold with Federer four years ago.
"Thank you for giving me the honour of carrying the Swiss flag. It's a moment of immense pride for me," the 27-year-old said on Twitter.
Wawrinka is the latest tennis player to be handed their country's flag for the opening ceremony.
Novak Djokovic will lead in the Serbia team, Maria Sharapova will carry the Russian flag while Wimbledon runner-up Agnieszka Radwanska has the honour for Poland.
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Defending men's champion Rafael Nadal had been due to be Spain's flag-bearer, but he has pulled out with injury.