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.
"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."
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.
"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," he added. "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."
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 (on Wendesday) and he was talking with West Ham.
"I don't know the total ins and outs of that (Cole's pay-off)."
- Sports & Recreation