Gerrard has spent the whole of his career at Anfield and remains a key part of Rodgers' plans as he prepares for the new season.
"I'm absolutely delighted, as you can imagine," said Rodgers.
"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.
"I think he's still got a good few years left yet. His level of performance last year was outstanding.
"He's been a great support for me coming into such a club, a brilliant captain, he's got great values and the leadership he provides is second to none.
"Now he can really concentrate on his football and hopefully stay at the level he's been at."
Rodgers admitted he enjoys a strong working relationship with England international Gerrard, who has scored 159 goals in 630 appearances for Liverpool.
"I respect his loyalty and he respects that I am the manager of the football club and make football decisions, but will talk with him," added Rodgers.
"I always work closely with players. We have a good relationship and the door is always open for Steven as the club captain.
"He's the current England captain and one of the best players to ever have graced the Premier League.
"To retain the humility that he has and still have the eagerness to want to improve and be better, he is a real shining light and example for many players."