The 39-year-old left Swansea for Anfield after a compensation package was agreed between the two clubs.
"I'm very proud, it's a club with wonderful tradition and I feel very blessed with the opportunity to manage the club," Rodgers said at his unveiling on Friday morning.
Rodgers admitted his mind was made up to move to Merseyside once it became clear he was the club's preferred target, saying: "Once I had found out I was the number one target from the important people at Liverpool it was quite an easy decision."
Liverpool is a step up for Rodgers from his previous jobs at Watford, Reading and Swansea. He also worked under Jose Mourinho at Chelsea and insisted claims he was too inexperienced for the role were unfair.
"My pathway as a young coach has been different to most managers," he said. "I have actually been coaching and working in football for 20 years. At Chelsea I had experience of working with big players.
"I look at Kenny Dalglish, he was the manager (of Liverpool in 1985) at 34 and resigned at 39. I arrive here at 39."
Liverpool chairman Tom Werner claimed Rodgers would bring "attacking, relentless football" to the club.
"In Brendan we have acquired a very exciting and talented and young manager," the American said. "He's a forward-thinking coach at the forefront of a generation of young managers and will bring to Liverpool attacking, relentless football."
Werner added: "We did speak to a number of people in the last few weeks, but I want to say Brendan was the only person we made an offer to. He was our first choice and the right choice."
Source: PA
Source: PA