The 23-year-old made the £12m move to Merseyside having left Manchester City to join Chelsea in 2009, and with little impact at both clubs, he is looking to prove his worth to Reds boss Brendan Rodgers.
The club has struggled with consistency under Rodgers this season, but Gerrard believes Anfield is the perfect place for Sturridge if he turns his potential into regular goals.
The England captain said: "Daniel has the quality. I know he's got it - I've seen it.
"He's suffered a bit at Manchester City and moved on to Chelsea where he hasn't played as much as he wanted but has shown flashes of brilliance.
"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.
"If he can start producing that for us on a weekly basis he can help this club move forward to where we want to be.
"He has said he wants to play football for a big club, the stage is set for him.
"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.
"He's at an age now where he should be performing week in week out."
Sturridge is likely to be Rodgers' main signing of the January window and has been brought in to offer support to leading scorer Luis Suarez.
The Uruguay international's stunning run of form shows no sign of decline as two goals in Wednesday night's 3-0 win over Sunderland took him to 15 in the league so far this season.
Gerrard believes the addition of Sturridge will improve Liverpool's hopes of a top-four challenge, adding: "Daniel's arrival will help the club. He's got power, pace, strength - he has got huge potential.
"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.
"He will add more strength in depth for us and let's hope he's not the last face in January because we certainly need a couple more in."
Suarez lit up Anfield with his two goals, after 18-year-old Raheem Sterling had opened the scoring, and Gerrard admits his team-mate is one of the best around at the moment as he trails Manchester United's Robin van Persie (16) by one in the Premier League top scorers chart.
"He's just world class. There are a handful of players in the world who operate on a different level and he is one of them," he said.
"He can score all types of goals. I was looking in the programme at his goal record: for someone who the critics say doesn't score enough, just have a look at his record (Suarez has scored 31 in 64 league games)."