Hodgson, who joined Liverpool from Fulham in July last year, had been under intense pressure after several humiliating defeats, culminating in a 3-1 debacle at Blackburn Rovers in the Premier League on Wednesday.
He leaves with the club four points above the relegation zone in 12th place, having won just seven of 20 league games, and on the day before Liverpool visit arch-rivals Manchester United for an FA Cup third-round match.
Liverpool's fans, long considered among the most loyal in the game, had chanted for Hodgson's dismissal and swamped radio shows and internet forums with tales of their disenchantment and criticism of his selections and tactics.
"It's a great honour to be asked to come back (albeit) in unfortunate circumstances. I will try my best," Dalglish told reporters on Saturday night after flying back from a family holiday in the Middle East to take over at Anfield.
"I have... found the last few months some of the most challenging of my career," he said on the club website.
"I am very sad not to have been able to put my stamp on the squad, to be given the time to bring new players into the club in this transfer window and to have been able to be part of the rebuilding process at Liverpool."
Former Liverpool player and assistant manager Phil Thompson said the fan pressure made Hodgson's position almost impossible.
"It has been very difficult for Roy to carry on. It is unprecedented in the way the fans have turned," he told Sky Sports News.
"Even in the dark days at the end of the (Graeme) Souness reign there were no chants for him to go. Liverpool fans felt as though we were different and we stick together -- this was incredible what we've seen."
It has certainly been a season of discontent for the supporters, who began it by campaigning against the club's previous owners George Gillett and Tom Hicks.
In a statement on the website Henry said: "Both parties thought it in the best interests of the club that he stand down," but the League Managers Association issued a statement saying Hodgson had wanted to continue in the job.
"He has not walked away, he was happy to carry on b
