Player-coach Leon Britton had been in temporary charge of Swansea since the Premier League's bottom side sacked Paul Clement on 20 December.
Carvalhal, 52, was dismissed by Wednesday on Christmas Eve, with the Owls 15th in the Championship table.
Carvalhal's first game in charge of Swansea will be at Watford in the Premier League on Saturday (15:00 GMT).
The Swans are hopeful Carvalhal will be able to inspire a transformation in their fortunes similar to the end of last season.
"Carlos' time at Sheffield Wednesday highlighted that he has great character and personality to lead the squad and the football club, which is vital at such a crucial time," Jenkins added.
"He has built up a lot of experience over the years which will ensure the team is structured and organised.
"He is driven and ambitious and while he has a big challenge ahead of him, I know he will tackle it without fear."
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