Hodgson was confirmed as new Liverpool manager on Thursday morning.
Gerrard said: “The club have made a good appointment in Roy Hodgson.
“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.”
