A club statement released on Tuesday evening read: "Swansea City and manager Michael Laudrup have tonight parted company.
"Garry Monk will take up the reins as head coach alongside current first team coach Alan Curtis for the foreseeable future.
"The club will be making no further comment at this stage, but will endeavour to keep our supporters updated with any future development."
One of Denmark's greatest-ever footballers, Laudrup moved into management at the end of his career and took charge of Swansea in the summer of 2012, after stints at Brondby, Getafe, Spartak Moscow and Mallorca.
The 49-year-old enjoyed an incredible first season in Wales, leading Swansea to Capital One Cup glory and ninth in the Premier League.
The Swans are currently 12th in the table but the congested nature of the bottom half of the Premier League means they are just two points clear of the drop zone following Saturday's 2-0 loss at West Ham.
And Laudrup, who signed a new contract in March 2013, has been coming under increasing pressure of late, with the Swans having won just one of their last 10 Premier League games.
Chairman Huw Jenkins said of the decision: "It is a decision we have taken reluctantly.
"But it's a decision made in the best interests of Swansea City Football Club and our supporters. It is the first time in nearly 10 years that the club has parted with a manager in this way, but we had to remove the constant uncertainty surrounding the club and Michael's long-term future with us.
"I had a meeting with Michael today in a final attempt to support him and establish a way to improve the work of the backroom team to secure the results we need over the final 14 Premier League games.
"However, after thinking long and hard about the best way forward, I felt it was unlikely we would achieve a stable environment at the club to allow us to get back to basics and produce the performance levels that have served Swansea City so well over the last few years.
"Now we need to put that uncertainty behind us and move forward as a united football club on all fronts, while placing on record our gratitude to Michael for the work he has done over the last 18 months and wish him well for the future.
"I hope all our supporters can fully understand how difficult this period has been for us and I would urge everyone connected to the football club to get behind Garry Monk, the staff and players."