The Dane has enjoyed a superb first season in charge of the Swans, guiding them to Capital One Cup glory and a place in the top half of the Premier League table.
The former Barcelona midfielder's initial deal was set to run out at the end of next season, but his decision to extend his contract through to June 2015 will alleviate fears he would depart for pastures new this summer.
"We've started something this season that I want to continue," Laudrup told the club's official website.
"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 has found himself linked with Real Madrid, Chelsea and Manchester City, and a recent poll of the fans of the Spanish giants showed 72 per cent wanted him to succeed Jose Mourinho at the Bernabeu.
But with a Europa League campaign lying ahead for Swansea next season, Laudrup wants to carry on the good work he has started.
"I am delighted to sign the new deal and I'm already really looking forward to next season," he said.
"I hope there will be some very exciting things happening with the team and with the club in Europe."
Swansea chairman Huw Jenkins had long made clear his desire to tie Laudrup to a longer-term deal and provide the club with more security.
Jenkins was particularly wary having seen Roberto Martinez, Paulo Sousa and Brendan Rodgers all leave the south Wales club during their climb through the leagues.
And he is delighted to have agreed terms with his manager as Swansea enjoy arguably the finest season in their 101-year history.
"This is a major boost for everyone involved with Swansea City, from the players, staff and board of directors through to the most important people of all, our supporters," said Jenkins.
"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, but I think everyone has seen for themselves that Michael has helped take this football club to another level.
"He is a pleasure to work with because he shares the same philosophy as everyone at this football club. He has ensured that we have progressed again this season and I am convinced his knowledge, experience and expertise will ensure we keep moving forward for the next few years."
Laudrup's contract extension is just the latest in a string of new contracts the club have agreed with key personnel.
The likes of top scorer Michu, Leon Britton, Ashley Williams, Wayne Routledge, Ben Davies and Garry Monk have all agreed new deals during the course of the current season.
Full-back Angel Rangel is another to have agreed terms after the club announced a new three-year deal for the Spaniard, securing his services until the summer of 2016.
Rangel said: "I am settled here, I am enjoying my football, I have married a Welsh girl and I'm building a house in Swansea - I feel like a Welshman now.
"I am very happy on a personal and professional level."
It seems the questions left unanswered in the "Swans prepare for Laudrup exit" article from the 3rd, have kindly been answered here. After capitalising on rather innocuous quotes, I'm glad this matter has been cleared up. How are they preparing to deal with the "Laudrup exit"? Oh, he isn't exiting, and has signed a new contract. I'm glad the media don't make a habit of 2+2=5 "he's on the way out the door" stories.- markarogers