Gerrard says he is looking forward to reuniting with Hodgson, having played under him during his spell in charge at Anfield. Hodgson was sacked as Liverpool manager in January 2011 following a dismal spell in which the team won 13 of 31 games in all competitions, but Gerrard believes Hodgson can be a success with England if he is shown patience.
"I've worked with Roy," said Gerrard. "He's a good man and a good manager. It's important he's given a chance and I'm looking forward to working with him again."
Hodgson, though, refused to commit to naming Gerrard as a replacement captain for John Terry after the Chelsea defender lost the armband over allegations he racially abused Anton Ferdinand in a league match earlier this season.
"Will Gerrard be England captain? That's another thing that will have to be carefully thought out. It's one of the things that will occupy my time in the days ahead," Hodgson said.
Gerrard was joined in welcoming Hodgson by fellow England midfielder Jack Wilshere, who will miss the upcoming Euro 2012 tournament through injury.
"For England....good choice in my opinion! Good luck and I hope I can help him in some way in the future!" Wilshere tweeted.
Manchester City's Gareth Barry said he was pleased, though a little surprised, by the FA's decision to select Hodgson over Tottenham boss Harry Redknapp, who was understood to be the favourite to take the reins following Fabio Capello's exit in February.
"Such a big thing was made about Harry, everyone else was forgotten," Barry told BBC Sport. "There probably were two runners, Harry and Roy.
"Roy was probably overlooked by the media but they've gone with him and let's see what happens. I've never met the new England manager and don't really know too much about him."