Hodgson has signed a three-year deal to succeed Rafael Benitez in the Anfield hot-seat and is hoping to get the Merseysiders back in the top four.
He said: "This is a very big club, a club with enormous tradition and when the club is sold it will get stronger rather than weaker.
"My priority is to try to get the team doing better than last season and get them back into the Champions League spots."
Hodgson led Fulham into the final of the Europa League last season and felt now was a good time to make the step up to a club with greater expectation.
He added: "It is the right move for me at this stage of my career.
"I am here on merit, I know the club did their homework before asking me to be their manager and my aim is to work for the club and the people of Liverpool."
One of Hodgson's first tasks will be to meet experienced campaigners Steven Gerrard and Jamie Carragher this afternoon.
"I am anxious to meet them," he said. "They are two key players and two key players in my future at this club.
"I need to know how they feel and talk to them about general things."
Hodgson had been mentioned as a possible replacement for England boss Fabio Capello, should the Football Association decide to end the Italian's contract early.
The FA are due to make a decision on Capello's position in the next fortnight, but Hodgson did not consider waiting to discover whether the England job become available before agreeing to take over at Anfield.
"No, that wasn't the case to be honest," he added.
"When this job was first discussed with me there was no idea that there might be a change in the England set-up.
"Also as a second point I don't expect a change in the England set-up. Thirdly there was never a case of me thinking of holding on and hedging my bets about that because I wanted to be here.
"The only question in my mind, after Liverpool had completed the due process to decide on who would be the manager, was whether or not it would be me."
The former Fulham boss was unwilling to discuss the transfer funds likely to be available to him, with suggestions he will have to sell players to bring some in because of the club's financial state.
"It's not the right time to talk about that," he said.
"It's a bit disappointing that the matters of money have been spoken about over football on my first day.
"I took this job because I wanted to be manager of Liverpool. I want to benefit from the huge fan base and the incredible support.
"I wanted to be part of that. I'd like to sign off on the financial part and leave that to the man sat beside me (chairman) Martin Broughton because he knows more about these things than me."
Captain Steven Gerrard and Fernando Torres are the high-profile names who have been linked with moves away and while Hodgson could give no guarantee they would remain, he said he would endeavour to keep them on Merseyside.
"It's very important for the club. That's the first thing," he said.
"I personally can't nail their feet to the floor. I'll try to convince them that if they stay here and have a good season then it's a good club to play for.
"It's out of my hands to an extent, but I do know the club is anxious to keep the players, I'm anxious to keep the players.
"We'll do all in our power to keep them. The fans are intelligent and know the situation. They can't expect me to give guarantees they'll stay on."
Hodgson's desire to keep his star names was backed by Broughton, who added: "They are not for sale. We don't need the money."
Hodgson continued: "I would be disappointed if the supporters were happy to survive on goal difference - I expect them and the club to crave these things (trophies) and it's our job to deliver where it matters.
"You can talk until you are blue in the face but it's what we do on a Saturday or Sunday afternoon that counts.
"The ambitions of the club should always be of the very, very highest level and that's what we're aspiring to.
"I'm here for the long haul to do the job that needs to be done - hopefully winning trophies very, very quickly. If not I have to hope the club has patience with me and gives me the chance to put it right the following season."
Asked if he saw the club as bigger than Inter Milan, one of the clubs he has previously managed, Hodgson was keen not to offend the Italian club's owner.
Hodgson said: "Making comparisons with Inter would be very harsh - I don't want to make that comparison because I am friends with Massimo Moratti.
"It's (Liverpool) as big, there's no doubt about that and certainly the challenge is as big as when I went to Inter."
He was grateful to Fulham for enabling him to make the move with the minimum fuss.
Hodgson said: "Fulham were good enough to let me speak to Liverpool and respectfully take the job.the conversation with the chairman wasn't pleasant from my point of view and I hope one day he'll forgive me.
"I had wonderful support there from Mohamed Al Fayed and I've said I don't want go in and raid them.
"When it comes to what players we need and how we strengthen the squad I'll leave that question until a later date because I haven't had time to sit down with Kenny Dalglish, Eduardo (Macia), Sammy Lee, the chairman and the chief executive to say 'what do we need?'.
"I need to canvass their opinions of what's been going on."
Broughton added: "We'd like to thank Mohamed Al Fayed and Fulham for being so good in the whole process.
"Being the LMA manager of the year shows the respect his (Hodgson's) peers have for him. That's been earned not just in the last year but over a long period of time.
"Roy brings experience, he's dealt with lots of international players in different teams. He's someone to steady the ship at this stage. He's got all the talents."
On a potential takeover of the club, he added: "Information has gone out to a number of people who have expressed an interest.
"There haven't been any offers to turn down but we wouldn't expect any offers at this stage.
"There is no specific deadline but hopefully a deal can get done before the end of the transfer season (August).
"But these things can take quite a bit of time. We're on course pretty well to be where we expected to be at this stage."
Broughton also clarified the situation regarding Kenny Dalglish by revealing the man who won the double for Liverpool in his first year in charge in 1986 was never a candidate this time round.
Club ambassador Dalglish was asked to advise on Benitez's successor and put his own name forward.
But Broughton said: "Kenny put his name in for the job and we appreciated the fact he wanted to do it but he was never a candidate.
"He is happy in his current ambassadorial role."