Dalglish took over the job from Roy Hodgson in January in a caretaker capacity with Liverpool 12th in the standings and four points above the relegation zone.
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They have climbed to fifth going into the final two games of the season and are favourites to qualify for the Europa League.
Steve Clarke, Dalglish's first appointment, has also agreed a three-year contract as first-team coach.
"It's a great reward for the work that's been done, not just by me but Steve, Sammy (Lee), the players and the people on the terraces and everyone else inside the club, including the owners," Dalglish told the club's website.
"We said at the outset if we stick together and work together then it makes it easier to produce better results and I think that is the main reason why results have improved."
The club's director of football Damien Comolli said they had not looked at other options.
"Kenny turned things around very quickly, with the help of Steve Clarke," he said. "For us, it was a no brainer.
"He hit the ground running from day one knowing what he wanted to do because he knew the boys anyway, especially the key players like Steven Gerrard and Jamie Carragher, and knew the young players in the academy."
The club's new American owners have also been impressed by the influence of Dalglish, a former Anfield favourite as a player and during his previous spell as manager.
"It was obvious very early on that the atmosphere surrounding the club has been transformed," John Henry said.
"No-one else could have produced such a response."
REMARKABLE TURNAROUND
It has been a remarkable turnaround under Dalglish.
Although they lost to Manchester United in the FA Cup in his first game in charge and were beaten in the league by Blackpool, the side quickly turned their form around.
After a draw with Everton they won four in a row, including an impressive victory at Chelsea, to fly up the standings.
At the end of January, Liverpool broke their transfer record twice in one day to buy strikers Luis Suarez and Andy Carroll following the sale of Fernando Torres to Chelsea, controversial deals that have since looked good business.
As well as getting the best from the club's established players, Dalglish has also blooded a new crop of youngsters, several of whom have come through the academy he used to oversee.
Liverpool's last five games have produced four wins and a draw at Arsenal to take them above Tottenham Hotspur, who they play on Sunday, and into fifth place. In the form table since the start of the year, only Chelsea are above them.
"When we came back in January there were no promises from anyone as to what to expect, so for me it was an ideal opportunity to go in and prove I had something to offer," Dalglish said.
"I never set any targets, but obviously we had to improve and we have done.
"But we can't afford to think that because we are finishing strongly that's us set up for next year.
"There won't be any complacency for next year because of what's happened this year." Liverpool won the last of their 18 league titles in 1990 and arch-rivals Manchester United are poised to overtake them, just one point away from wrapping up their 19th championship.
