The 23-year-old completed a long-term deal with the Reds on Wednesday and was in the stands to watch his new side comfortably beat Sunderland 3-0.
Having left Manchester City in the summer of 2009 with six goals in 32 senior appearances - the majority as substitute - he found life equally tough at Chelsea.
In 96 games for the Stamford Bridge club he hit 24 goals, although he still made only 31 Premier League starts in three and a half years.
His best spell was in a five-month loan period at Bolton, while they were still in the top flight, when he scored eight goals in 12 matches.
Rodgers hopes the England international can reproduce that form over a much longer period with Liverpool.
"He is a player that I've know since he was about 12 years of age," said the Reds boss.
"He made his name as a youngster at Manchester City when he was one of the top young strikers in European football.
"You make a move as a young player and it is always going to be difficult because what he is is a goalscorer and the only spell he's had that was at Bolton.
"When he has played games he has scored goals. He gives us that power, presence and mobility at the top end of the field and the biggest thing is hunger.
"We are bringing in a player who knows he has to perform if he wants to be at one of the biggest clubs in the world and this is probably his last chance.
"I have every faith that over his time here he will prove a real hit and it gives us another attacking threat at the top end of the field.
"Daniel will learn off the top players who are here."
As Sturridge was arriving midfielder Joe Cole was holding talks with West Ham over a permanent move after Liverpool agreed to pay off his £100,000-a-week contract to get him off the wage bill.
"I'm not sure a deal has been totally agreed," Rodgers said.
"I spoke to him a couple of times (yesterday) and he was talking with West Ham.
"I don't know the total ins and outs of that (Cole's pay-off)."
Captain Steven Gerrard agreed with his manager and said, at some point, the player had to realise his situation and turn potential into regular goals.
"Daniel has the quality. I know he's got it - I've seen it," said the England captain.
"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 hot run of form shows no signs of abating as two goals in last night's 3-0 win over Sunderland took him to 15 in the Premier League so far.
But with fellow forward Fabio Borini edging closer to a first-team return Gerrard believes the addition of Sturridge also will improve their hopes of a top-four challenge.
"Daniel's arrival will help the club. He's got power, pace, strength - he has got huge potential," added the midfielder.
"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)."