Former Swans captain Monk's three-year deal sees him succeed revered bosses like Roberto Martinez, Brendan Rodgers and Michael Laudrup at the Liberty Stadium.
He was named in temporary charge after Laudrup departed the club earlier this season before Swansea decided he was the man to take them forward on a long-term basis
"I feel very honoured," Monk told reporters on Friday.
"It is something I have always dreamed about doing
I didn't expect it to come this soon, and it is an opportunity I intend to take.
"I've lived in this city for 10 years
I have always tried my hardest for the club, so it never felt like a trial.
"You are there to be judged
I expect that
It doesn't faze me at all
I have a plan in my own head of what I want to do and how to go about it.
"I want to take the club forward
I have been part of the 10-year journey with this club, and now it is about improving on that, which is what I will be looking to do."
Monk's first task - after Sunday's Barclays Premier League finale at Sunderland - will be to keep working on the squad he would like in place for next term.
"Players will go and players will come
I think players understand that, and clubs understand that," he added.
"You will be constantly linked with players when you are in the Premier League
I think it's just a case of us working closely together and making sure we get the targets we want to get.
"As a club, you have to be looking at all sorts of players, and that is what we have been doing
In the coming weeks, I guess we will narrow it down."
Monk constantly straight-batted questions about his future in recent weeks, and he admitted that it was not until after top-flight safety was secured did he even contemplate focusing on himself.
"It is not about me, it was about the situation that we were in, me coming in and making sure that the team got across the line," he said.
"I think it has only been since the Aston Villa game (last month) that I have turned my thoughts to myself.
"We really want to finish off with a positive result for our fans and ourselves on Sunday.
"We were disappointed last week (against Southampton)
We deserved at least a point, and to come away with nothing was hard to take
We need a reaction."
Swansea's chairman Huw Jenkins said Monk's longevity with the club had been a key factor behind his appointment.
"Garry's experience of working with us as a football club is vital," he said.
"We feel one of the most important ingredients of appointing any manager is making sure you have got people with you that can work together and for the football club
They are the qualities he has.
"There is always that difficulty of somebody coming in during the season
Now that we have got this set in motion for next season, he has got all pre-season to work with the players and that is a massive thing going forward.
"We fought a battle for 10 years against all the odds to achieve what we achieved, and we have got to make sure that we collectively have got that belief going forward that we can defy the odds.
"I think Garry is accustomed to that - I think that will be embedded in our players going forward.
"We have all been doing this long enough to realise that staying in the Premier League is number one
Some of our fans might think that is defeatist, but I think it is just realism of the level we are playing at.
"The challenge exists to stay in the Premier League and secondly we have always got an inner belief that every game we play we can go out and win, and we will see where that takes us.
"The reason we have been successful is that we have always been fighting against the odds since we got promoted to the Premier League.
"The moment we get complacent, we will go backwards
Every year has got to be a challenge and a fight - we know that
The more we challenge and fight, the higher we will finish up the league."
Source : PA
Source: PA