Gerrard - along with Fernando Torres - has been linked with a move away from Anfield this summer, with Real Madrid said to be among his suitors.
But after Hodgson revealed the midfielder had played a key role in luring Joe Cole to the club, Gerrard says it will be "fantastic to play alongside him in a red shirt for Liverpool".
He added in the Liverpool Echo: "It is a great signing for us. I know Joe well through the England set-up and have seen first hand just how good a player he is.
"I've told him what a great club this is and I'm sure Joe's the sort of exciting talent our fans will love to see."
Of his own future, he said: "I made it clear that I simply needed to concentrate on the World Cup and then have a decent holiday with my family.
"I wanted the chance to meet Roy Hodgson privately and having done so, I'm very impressed with his plans for the future."
News of Gerrard's commitment has been welcomed by Hodgson, who said: "It's a great piece of news.
"There won't be anyone in Liverpool today who isn't delighted to hear that.
"I'm really pleased about it because I've got great respect for Steven Gerrard.
"He's a player who I was really looking forward to working with when I came to Liverpool.
"It seems now with that commitment that this will happen. It gives everyone a boost without question.
"It will be a tough season, with a lot of matches and the disappointment of last season is going to take a while to dissipate, but it is very good that our best player is still going to be playing at this club.
"Hopefully with the signing of Joe Cole - and if we are lucky one or two others, to boost the squad - we will be going into this season's competition, maybe stronger on paper than we were last season."