The 31-year-old captain, who has spent his entire career at Anfield, put pen to paper on the undisclosed terms on Thursday.
"For us, for Steven and for everybody connected with football club it's fantastic news," Dalglish told the club's official website.
"We're delighted for him and are looking forward to him getting back to full fitness and working hard for us and with us.
"He's been a fantastic servant to the football club."
Gerrard has made 393 appearances for the Reds since his debut in 1998.