Benitez, who had four years of his five-year contract to run, finalised his departure after agreeing a severance payment and said he was "extremely sad" to be leaving the club.
"I'll always keep in my heart the good times I've had here, the strong and loyal support of the fans in the tough times and the love from Liverpool," he told the club's website.
"I have no words to thank you enough for all these years and I am very proud to say that I was your manager.
Recently-appointed club chairman Martin Broughton thanked Benitez for his efforts, but said it was time for a new era.
"Rafa will forever be part of Liverpool folklore after bringing home the Champions League following the epic final in Istanbul but after a disappointing season both parties felt a fresh start would be best for all concerned," he said.
Former Valencia coach Benitez had been linked with Real Madrid and Juventus in recent months, but with both those clubs now having new men in charge he could be in the running to fill the vacant position at European champions Inter Milan following the departure of Jose Mourinho.
One thing that could delay the appointment of a permanent successor to Benitez at Anfield is the uncertainty over the club's future ownership.
Liverpool are £351m in debt and were put up for sale by co-owners Tom Hicks and George Gillett earlier this year.
The American pair's ownership of the Reds has been a long-running source of discontent for many fans, who are unhappy with the way the club is being run, and there have been regular protests and public disputes.
Benitez had a fractious relationship with the pair, who admitted sounding out former Germany coach Jurgen Klinsmann about the possibility of taking over from Benitez at the end of 2007, when they feared he could leave the club.
BBC Sport understands that Dalglish is unlikely to play a role in the future management of the club, and the Reds are happy for Benitez's assistant Sammy Lee to take the reins until after the World Cup if necessary.
Fulham manager Roy Hodgson and Aston Villa boss Martin O'Neill have been mentioned as potential targets to take over in the long term, as has former Chelsea manager Guus Hiddink, although he recently signed a contract to become coach of the Turkish national side.
But whoever takes the job may have to accept that major additions to the squad are unlikely without first selling players, with BBC Sports News correspondent Dan Roan will have a summer transfer budget of between £10m and £15m.
The lack of cash available to invest in players has led to fears over the futures of some of the club's main assets, with striker Fernando Torres and captain Steven Gerrard linked with possible moves.
Former Liverpool defender Mark Lawrenson told BBC Sport that Benitez's biggest legacy would be the memory of the team's miraculous comeback to win the 2005 Champions League final.
But Lawrenson said that ultimately Benitez was brought down by his failure to have cover for key striker Fernando Torres when he got injured last season.
"He will be remember for that unbelievable European Cup win when they came from 3-0 down to beat Milan, which came very early and how fantastic that was, but he slipped up last year," he said.
"He didn't have a good enough replacement for Torres, and the season fell flat on its face."
In addition to that famous victory in Istanbul, Benitez brought the FA Cup to Anfield in 2006 when captain Steven Gerrard produced a magnificent performance to help the Reds edge past West Ham on penalties.
But the Premier League title, the prize so desperately wanted by Liverpool fans forced to watch bitter rivals Manchester United gradually draw level with their haul of 18 championships, proved beyond Benitez.
