Hodgson was Liverpool's first choice to replace Rafael Benitez after the 62-year-old enjoyed a couple of impressive seasons at Fulham, which culminated in them reaching last season's Europa League final.
Hodgson admitted it had been difficult to leave the west London club, where he had built up a bank of goodwill, but believes taking on the Anfield job will be a highlight of his long and varied managerial career that has included stints in charge of Inter Milan, Blackburn and the Finland national team.
His appointment, on a three-year contract, has already received the backing of club captain Steven Gerrard, and Hodgson is keen to begin the job of reviving the club's on-field fortunes after they finished seventh in the Premier League table last term.
"I'm extremely proud. The club's tradition in terms of its football and its managers is really second to none and it was an opportunity which was absolutely impossible to turn down," Hodgson told the Reds' official website.
"I am both proud and excited at the prospect of working as the Liverpool manager.
"I don't think there are many jobs that would have tempted me away from Fulham, to be perfectly honest.
"I had such a good relationship with the chairman and the chief executive, the players were magnificent to work with and everything was as good as it gets, but on the other hand when there was a chance that Liverpool wanted me, and they asked to speak to me, I asked the chairman for permission.
"He wasn't too happy to give it but fortunately for me this job came about and I am really happy to be here.
"It'd be foolish to compare but it'd also be dishonest to say anything other than it's going to be a highlight of my career.
"I have worked long and hard to reach the level I have reached."
Hodgson arrived at the club's Melwood training ground this morning to meet those players who had returned for the first day of pre-season, although many of the club's stars are still on leave after playing at the World Cup.
He will give his first press conference at 1.30pm at Anfield this afternoon before meeting with senior players such as Gerrard and Jamie Carragher.
With the futures of Gerrard and star striker Fernando Torres at Anfield a matter of some uncertainty, Hodgson said it would be an immediate priority to ensure they remained.
"It's important, of course. I don't think there's anybody here at the club who would welcome losing them," he said.
"Certainly the fans wouldn't welcome losing them and us as a club I'm sure will do everything we can to make certain they stay with us.
"I'll be trying to persuade them that this is the place to be. I'll ask them to give me a chance to work with you and give us a chance to improve on last season.
"It would be foolish to give guarantees that it's going to happen because I can't speak for the players themselves, but I'll be doing my best to keep them."
He added: "There are a couple of meetings this afternoon with senior players, in particular Steven and Jamie, and I'll contact the rest by telephone.
"I will make certain that before the end of the week I have had a conversation with all of the players to tell them I'm here and am looking forward to welcoming them back when they come."
Hodgson's hopes of keeping Gerrard would, however, seem strengthened after the midfielder endorsed his appointment this morning.
"The club have made a good appointment in Roy Hodgson," added Gerrard.
"Rafa left a few weeks ago and I know the club were determined to take their time and get the right man for the job.
"Roy is hugely experienced and I believe he is the right man for Liverpool.
"I think it's been worth the wait and I'm sure he's just keen now to get on with it and start to quickly put in place his plans for the new season."