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 in 2011 where he scored eight goals in 12 matches and Rodgers hopes the England international can reproduce that form.
"He is a player that I've know since he was about 12 years of age," said Rodgers. "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."