The 33-year-old midfielder signed a new deal until 2015 on Monday.
"I'm absolutely delighted, as you can imagine," Sky Sports News quotes Rodgers as saying.
"I've talked throughout pre-season about wanting to bring other players into the group, but this was one of the - if not the - most important signings for us.
"He's an icon here at the football club - a real iconic figure for players and supporters."
Gerrard has scored 159 goals in 630 appearances for Liverpool following his debut in 1998.