The 34-year-old, who has captained the Welsh club in all four divisions, took the reins on Tuesday following the sacking of Michael Laudrup with the Swans sitting just two points clear of the drop zone.
The Swans are currently 7/1 to suffer relegation from the Premier League with Paddy Power, but Monk told the club's official website: "I will give everything I have for Swansea City. 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 has 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. I also know how important this football club is to the fans. 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."
Laudrup and his assistant Morten Wieghorst were shown the door after a poor run of form that saw the Swans record just one victory in their last 10 Premier League games.