Monk took the reins for the "foreseeable future" after Michael Laudrup's dismissal on Tuesday, with the Dane's backroom staff - assistant manager Morten Wieghorst, fitness coach Oscar Garcia and overseas scout Erik Larsen - also leaving.
And Monk, who spent 10 years at Swansea as a player, has vowed that he and his players are fully committed to keeping the Welsh club in the top flight after a run of just one win in their last 10 Premier League games.
"I will give everything I have for Swansea City," the 34-year-old told Swansea's official website.
"I will promise the fans that. And I will ensure the players do exactly the same. We are all in this together - and I will make sure we stick together.
"That is what Swansea City have been all about for as long as I can remember.
"I know this club inside out and I will try and use that knowledge to the betterment of Swansea City."
Monk, who captained Swansea in all four divisions after signing from Barnsley in 2004, went on to say it was vital that the club battled for the supporters.
"I know how important this football club is to the fans," he added.
"They are the important ones in all this and we will all fight every inch of the way for them.
"This is a proud moment for me, and I aim to do the best possible for this club and the loyal supporters."
Monk will be assisted by Alan Curtis, who has been at the club in a playing and staff capacity for 30 years.
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