Laudrup has made a huge impact since taking over the reins at the Liberty Stadium in the summer.
The Dane guided the Swans to their first major trophy when they lifted the Capital One Cup with a 5-0 victory over Bradford at Wembley last month.
That win will see Swansea compete in the Europa League next term and with the south Wales club currently sitting in eighth in the Premier League, they are set to be playing in the top flight for a third successive season.
"We've started something this season that I want to continue," Laudrup, who has been linked with Manchester City, Chelsea and Real Madrid, 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.
"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.''
Swansea chairman Huw Jenkins added: "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.
"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.''