The captain signed a new two-year deal on Monday with a view to ending his career at Anfield, ahead of his 16th season in professional football with the club.
And Rodgers could not hide his delight after Gerrard had put pen to paper, stating that the England international is his most important signing this summer.
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"He's an icon here at the football club, a real iconic figure for players and supporters. Also, importantly, his contribution at this moment in time is very much valued by myself and the staff.
"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."
Rodgers also admitted he enjoys a strong working relationship with Gerrard, who featured in all but two of Liverpool's Premier League games last season.
"I respect everything he's done within the game prior to me coming in here," Rodgers added. "I respect his loyalty and he respects that I am the manager of the football club and make football decisions.
"I always work closely with players. We have a good relationship and the door is always open for Steven as the club captain.
"He and I speak regularly and our relationship is very, very good, as it is for me with most of the players."