City's top scorer, who cost just £2.2m when he arrived from Rayo Vallecano in July, was previously contracted until 2015.
The extended deal will strengthen Swansea's hand if they are forced to field enquiries this summer for a player who has scored 13 Premier League goals in his first season, prompting speculation he might move on to a wealthier club.
Michael Laudrup said this month it would take a huge offer to land "the bargain of the season", and Michu told the Swansea website he is in no rush to go anywhere.
"It was an easy decision for me," he said. "I am living a dream here at Swansea. I'm probably enjoying my football more than ever.
"I'm really happy here in the city with the people, the club and the fans. I think the club are happy with me because they have given me a new contract. I am certainly happy with the club.
"I've read and listened to all the speculation, but it doesn't interest me, and that's why I've signed a new contract.
"I'm enjoying myself too much because the team always tries to play football. All I think about is the next game and helping Swansea be successful. This is my life."