"The main priority is to be successful and I want to achieve success at the club I love. If we can win more trophies together then I will be really happy."
A delighted Benitez said: "Steven has once again shown his commitment and it was an easy deal to agree. As soon as we offered him the option he said yes.
"There were no problems at all. He wants to stay for life.
"This deal sends out another clear message that we are moving forward as a club. To know we have a player of Steven's quality with us for many more years is a great boost for the club and the fans.
"He is clearly a player who inspires those around him and even though he is playing very well at the moment, I still think his best years are ahead of him."
Gerrard has been instrumental in recent weeks in Liverpool's bid to end their 19-year wait for a league title and is the club's top scorer this season with 22 goals in all competitions.
Liverpool have moved to within a point of Manchester United after an impressive 4-1 victory at Old Trafford last month, which was followed by an equally emphatic win as Gerrard scored a hat-trick in the 5-0 thrashing of Aston Villa at Anfield.
Victory away at Fulham on Saturday would see them move to the top of the Premier League, albeit possibly only for 24 hours as Manchester United host Villa on Sunday.
Benitez signed a new contract himself last month and since then he has been quick to tie down other members of his backroom team.
Assistant boss Sammy Lee and first team coach Mauricio Pellegrino agreed extensions of at least two years, while goalkeeping coach Xavi Valero, fitness coach Paco de Miguel and chief scout Eduardo Macia have also re-signed.
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