Laudrup was relieved of his duties following a poor run of form which has left the club just two points above the Barclays Premier League relegation zone.
The events occurred within a day of chairman Huw Jenkins dismissing rumours that they had discussed the future of the manager.
Speaking to swanseacity.net Monk vowed to "give everything" as he takes over the helm.
"I will promise the fans that. And I will ensure the players do exactly the same," Monk said.
"I know this club inside out and I will try and use that knowledge to the betterment of Swansea City."
Leaders Arsenal visit Champions League chasing Liverpool in the early kick-off on Saturday with the Gunners looking to maintain their two-point advantage over both Manchester City and Chelsea.
Manager Arsene Wenger, who tried to buy Luis Suarez last summer, has said it is crucial Arsenal starve the Uruguayan and his strike partner Daniel Sturridge of service.
Wenger told arsenal.com: "(The key is) for us to dominate the game and leave them as few balls as possible.
"That will be one of our targets of course.
"At Liverpool the task might be a bit more difficult but the philosophy on our side has to be the same - to master the ball and to have the ball and to dominate the game."
Fellow Champions League contenders Everton and Tottenham face off at White Hart Lane, the reverse fixture seeing the two sides play out a goalless draw.
Chelsea boss Jose Mourinho will hope his side can carry on where they left off at the Etihad Stadium - they beat Manchester City 1-0 - as they entertain Newcastle who are now without a director of football after Joe Kinnear resigned from the position on Monday.
Magpies boss Alan Pardew said: "I'm just sad to see anybody lose their job, as Joe has. He did a lot of good work here. My job is actually the next game and that's what I'm focusing on."
With Fulham rooted to the bottom of the table, Rene Meulensteen's team could give themselves a mountain to climb should they lose away Manchester United.
Fellow strugglers Crystal Palace and West Brom meet at Selhurst Park, the sides level on 23 points and each with a chance to put distance between themselves and the relegation zone.
Manchester City will be looking to bounce back at Norwich after their home loss to Chelsea, with Manuel Pellegrini set to turn to Stevan Jovetic to maintain City's title push in the absence of injured duo Sergio Aguero and Alvaro Negredo.
Elsewhere, Southampton host Stoke as relegation-threatened West Ham travel to Aston Villa.
The Hammers will be without star striker Andy Carroll after he lost his appeal to the Football Association against a three-match ban for brushing Chico Flores with an elbow in the 2-0 victory over Swansea.
In-form Sunderland host Hull, who drew at home to Tottenham in their last league outing to halt a run of four straight league defeats.