The Northern Irishman has signed the new deal, believed to take him through to 2018, which has been on the table since earlier in the season when the progress made under him began to transform into a title challenge.
While the Reds ultimately came up just short in the battle with Manchester City, a return to the Champions League is an important milestone and Rodgers believes it can provide the base for something even bigger.
"We'll now move into the next phase. We're into the Champions League. Our dream and goal is to win the Barclays Premier League - that's what we want to do," said the 41-year-old.
"We've shown this season that we can compete for that. With some new additions in the summer we believe that we can fight again.
"The objective for me was to try to get Liverpool established again as one of the leading clubs in European and domestic football and we're on course for that.
"We'll look to move forward again next season and over the coming seasons."
Rodgers had one year remaining on his current deal, with the option for a further 12-month extension, but developments this season guaranteed him new and improved terms.
Talk of the new contract began three months ago but Rodgers put any negotiations on hold, knowing full well the offer was there and he would accept it, in order to concentrate on the title run-in.
"It was very important for me (to wait until the season had finished)," he told Liverpool's official website.
"We were talking through the season but my focus was really on the team and the supporters.
"I wanted to just make sure we could focus entirely on what we were doing and on the job in hand - any contract talk we would speak on afterwards.
"There's still a lot of development in the club for me and it was always going to be straightforward once the season was finished because I love being at Liverpool.
"It's a huge privilege for me to manage this club and to have been offered the opportunity to carry on with the work I have been doing over the last couple of years.
"It leaves me hugely honoured. I'm absolutely delighted to be able to continue what has been a really exciting time for the club.
"We've got a bunch of players now that are very hungry, who are very committed to helping Liverpool."
Owners Fenway Sports Group have been impressed not only with the way Rodgers has improved the team without the need for numerous and expensive signings but with the manner in which he has handled himself during his two years in charge.
In a joint statement principal owner John Henry and chairman Tom Werner said: "We are very fortunate to have a hugely-talented individual leading our football performance and in whom we place our trust to deliver the vision we share for Liverpool Football Club.
"Brendan is at the heart of what we, as an ownership group, are trying to achieve on the pitch.
"This season has reaffirmed everyone's belief that we can bring football success to Liverpool and we are all committed to working together to achieve that."
Rodgers has always been quick to pay tribute to the support he has received from the American owners.
"I'm a great admirer of theirs and their honesty and how they have given me the opportunity to be here," he added.
"That has been key for me because, as a young manager coming into such a prestigious club, I was going to need that time to implement the ideas that I wanted to.
"One of the big reasons I came to Liverpool was because of them and hopefully they feel vindicated because of the work we have carried out over the last two years."
Planning for summer transfers continues but progress is slow in talks with Southampton for midfielder Adam Lallana, although Liverpool have been offered some encouragement in their pursuit of Bayer Leverkusen midfielder Emre Can despite the presence of a Bayern Munich buy-back clause.
"We're all working hard still in terms of looking to get players in," said Rodgers.
"Of course, at the club, where we are now the signings are complex; they are not all simple signings.
"But we need to strengthen up the squad and that's something that we're working hard to do over the next number of weeks."
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