The former Chelsea man moved to Anfield in a 12 million pound deal on Wednesday, with the Reds' skipper challenging the striker to prove his potential with the Merseyside club.
The England striker was in attendance as the Reds beat Sunderland 3-0 at Anfield on Wednesday evening, and the Liverpool skipper is looking forward to linking up with the 23-year-old.
"Daniel has the quality,” Gerrard told Sky Sports. “I know he's got it - I've seen it. He has said he wants to play football for a big club, the stage is set for him. He's at an age now where he should be performing week-in, week-out. There will be no excuses for him. He will be playing with good players at a great club.
"It's all there for him. He just has to go and grasp it with both hands. I think he's at the age now when he needs to settle down, get a settled club and show consistently what qualities he's got.
Sturridge scored a career-high 13 goals in all competitions for Chelsea last year and earned a place on Team Great Britain's Olympic roster, but he fell out of favor at Stamford Bridge this season. Sturridge enters Liverpool having played in just 12 games in all competitions in 2012-13 and netting just twice. The Reds will be hoping that Sturridge can replicate his 2011-12 form to provide a complement to in-form Uruguayan forward Luis Suarez.
"Daniel's arrival will help the club. He's got power, pace, strength - he has got huge potential," Gerrard said. "He's another attacking option, and if you look at the bigger picture from the beginning of the season up until now, we have been a little bit short in the final third."