Gordon Brown has led the praise for the Metropolitan Police commissioner.
The Prime Minister said in a statement: "Sir Ian Blair has made a huge personal contribution to the safety and security of our country, leading the national police effort against terrorism and the fight against crime, successfully introducing neighbourhood policing in London and cutting crime in the capital very significantly.
"I congratulate him and his officers, and of course I want to pay particular tribute to Sir Ian's leadership when London experienced the most serious terrorist attacks ever on British soil."
Home Secretary Jacqui Smith accepted Sir Ian's resignation with reluctance - but the Conservatives welcomed the move.
The Tories repeatedly called for him to stand down after the Metropolitan Police was found guilty last year of serious failures that led to the death of innocent Brazilian Jean Charles de Menezes.
Ms Smith said she accepted Sir Ian's decision to quit "with regret".
"Sir Ian has always had my support for the demanding and vital tasks that we expect of the Met," she said.
But shadow home secretary Dominic Grieve accused the Government of showing a "serious lack of judgment" about the leadership of the Met. He said: "This is the right decision.
"We have been calling for Sir Ian to step down for almost a year - since the serial and systematic failings at the Metropolitan Police disclosed during the de Menezes trial - whilst Cabinet ministers from the Prime Minister onwards continued to express total confidence in him.
"It is vital that a successor is appointed who can restore public confidence."
