The 23-year-old completed a £12 million move from Chelsea last week before making a goalscoring debut in Sunday's 2-1 FA Cup win over Mansfield.
And the Birmingham-born forward could not hide his excitement at being given the opportunity to join the Reds following a frustrating time at Stamford Bridge.
"It is the biggest club I have ever played for. In the Premier League, there is no bigger club than Liverpool," he told the club's official website.
"I thank the boss for giving me an opportunity to play for a club like this and I thank God for making it possible.
"It's amazing for the manager to put such faith in me. The only way I can repay him is by doing a job on the football field.
"For him to pay money for me and to have faith in me and show everybody around the world that he is prepared to take a chance on me, I don't think I'll ever be able to repay him for that.
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"So I'm grateful the manager has given me this chance and that he believes in me. I'm just glad to be here."
Sturridge was replaced by Luis Suarez 55 minutes into his first game, but hopes to strike up a partnership with the prolific Uruguayan in the future.
"It's going to be a pleasure for me to play with Luis," he added.
"He shows what a good player he is every time he gets the ball with the way he really gets at defenders.
"I'm looking forward to us forming a formidable partnership against the teams we've got coming up soon.
"I'd love to start against United but it's down to the manager which team he picks. I'm just here to train hard and whichever team he picks will be the one that is right tactically.
"If he chooses me then great, if not I'll be looking to come on and make an impact."