"I know there has been a lot of speculation [about my future], but I've always said that I am happy here and I never had any doubts I would stay," Laudrup said on the Premier League club's website.
Laudrup orchestrated Swansea's march to the League Cup trophy last month, which included defeating European champions Chelsea in the semi-finals and a record 5-0 win against fourth-tier Bradford City to clinch the title. Swansea are also eighth in the league.
Real Madrid were among the clubs the Dane had been linked with but as Swansea are assured a first foray into Europe next season in the Europa League, Laudrup said he was not going anywhere.
"We've started something this season that I want to continue," said the former Barcelona player and Denmark international.
"I am delighted to sign the new deal and I'm already really looking forward to next season. I hope there will be some very exciting things happening with the team and with the club in Europe," added the 48-year-old.
The former Getafe, Mallorca and Spartak Moscow manager signed a two-year contract last June when he replaced Brendan Rodgers who went to Liverpool.
Laudrup, who won four Spanish league titles in a row with Barcelona and Real from 1991-95, was acclaimed as Denmark's best ever player though he did not take part in his country's surprise 1992 European Championship win.
Swansea chairman Huw Jenkins said Laudrup's commitment was a major boost to the club.
"You can never guarantee how things will work out when you employ a new manager, especially after the success we've had in recent seasons," said Jenkins.
"I think everyone has seen for themselves that Michael has helped take this football club to another level."
