Faithful captain happy to continue working with coach Rodgers at Anfield.
Transfer talk: Gerrard extends stay at Liverpool but wants to see new faces
Gerrard, 33, who has spent his entire career at Anfield, signed a two-year deal at the club's Melwood training ground on Monday.
The England skipper told Liverpool's website: "I think everyone knows what it means to me.
"I've been here that long and so to extend, it's a big day for me and I'm really happy for myself and my family. It's great news.
"It lets me know the club thinks an awful lot of me and want me here.
"I'm glad it's all done and it's happened at the right time before the season, so I can just focus on playing as well as I can.
"I've got a lot of confidence and belief in my teammates and in the coaches we've got.
"Every fan out there and the players are no different - we want to see a few more faces to strengthen the team and squad even more.
In Brendan Rodgers' first season in charge last term, Liverpool finished seventh in the Premier League and so far this summer they have added to their squad by bringing in goalkeeper Simon Mignolet, defender Kolo Toure and forwards Luis Alberto and Iago Aspas.
Asked about his relationship with Rodgers, Gerrard - also the England captain - said: "I think it's perfect.
"I've loved every minute of working with him since he came through the door and I hope he is here for certainly the next couple of years. I want to work with him more.
"The relationship is growing and I feel as if he is the man to take this club forward."
Managing director Ian Ayre said the club and the player would review the contract situation in 2015, but was confident the new deal would secure the midfielder's services "until the end of his career".
Gerrard made his first-team debut in 1998 and has now racked up 630 appearances for the club, scoring 159 goals, and winning the 2005 Uefa Champions League, the 2001 Uefa Cup, two FA Cups and three League Cup crowns.
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