Gerrard worked with Hodgson during the 64-year-old's ill-fated spell in charge of Liverpool and has been tipped as a possible future England captain.
Gerrard said in a statement released to Press Association Sport: "I've worked with Roy. 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 dodged a question over whether Gerrard would replace John Terry after he lost the skipper's armband over allegations he racially abused Anton Ferdinand in a league match earlier this season.
Terry faces a court case in July when he will answer the charges, which he denies.
Speaking at a Football Association press conference at Wembley to announce his appointment, the new England manager said: "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."
Gerrard was joined in welcoming Hodgson by fellow midfielder Jack Wilshere who has missed much of Arsenal's season through injury.
Wilshere tweeted: "For England....good choice in my opinion! Good luck and I hope I can help him in some way in the future!"