Monk and first-team coach Alan Curtis oversaw their first training session on Wednesday after the Swans parted company with manager Michael Laudrup.
The Dane has been followed through the exit door by assistant manager Morten Wieghorst, fitness coach Oscar Garcia and overseas scout Erik Larsen ahead of Saturday's south Wales derby against Cardiff.
Laudrup's departure, announced on Tuesday night, has been backed by the Swansea City Supporters' Trust, with the club currently sitting just two points above the Barclays Premier League danger zone following a run of one win from 10 games.
Long-serving defender Monk, a former club captain, and Swansea stalwart Curtis have been put in charge "for the foreseeable future".
"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," Monk, 34, told Swansea's official website.
"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."
The Supporters' Trust, which has more than a 20 per cent shareholding of the football club, supported the decision and called on fans to get behind Monk and the players "in the tough battles ahead".
Monk faces a baptism of fire, with Swansea gearing up for a remaining February schedule of six games in 20 days - league appointments with Cardiff, Stoke and Liverpool, an FA Cup tie at Everton, plus home and away Europa League clashes against Napoli.
Trust chairman Phil Sumbler said the Trust had been aware of "growing concerns" among the Swansea board regarding Premier League performances.
In a statement, the Trust said: "During its tenure at the club, the current board, including a representative of the Supporters' Trust, has made key decisions which have taken the club forward, and ultimately we believe that this decision has been taken with the best interest of the club in mind."
And Sumbler added: "There has inevitably been a mixed reaction among fans to the announcement, with the club facing a critical period of key matches in three major competitions.
"However, we know from our supporter director Huw Cooze that the board has not taken this decision lightly, particularly in such an important week for the club, and it's vital that we now all pull together to give the team our full support.
"We all want to see an upturn in results, and what better place to start than at the Liberty Stadium against Cardiff City?"
The Trust has also placed on record its thanks to Laudrup for his achievements during his time at the club.
Despite Swansea winning the Capital One Cup during Laudrup's reign, his relationship with the club had reportedly been strained since a major disagreement over transfer policy last summer.
Laudrup, who had previously had managerial spells with four different clubs including Real Mallorca and Getafe, was appointed in 2012 as successor to Brendan Rodgers.
Problems first surfaced last summer when Laudrup and Swansea chairman Huw Jenkins fell out over transfer targets. The club subsequently opted to cut all ties with Laudrup's agent Bayram Tutumlu.
Press Association Sport understands tensions have also remained throughout the current season, and there has also been disquiet about the intensity of training sessions.
With Laudrup gone, and Monk and Curtis now heading up coaching operations, attention has already switched to who might become Laudrup's long-term successor, with former Swansea assistant manager and current Everton assistant Graeme Jones a strong candidate among bookmakers.
- Sports & Recreation
- Michael Laudrup
- Swansea City
- Premier League