The Prime Minister said that the allied forces were close to having all the elements in place for a peace agreement in the Kosovo conflict.
And he reassured MPs that the presence of 10,000 Russian troops would not amount to partition for the war-torn region because the force would be under unified control.
In his first Commons statement since the Whitsun recess, Mr Blair said the UN Security Council resolution brokered by the G8 countries would come under Chapter VII of the UN charter, which meant it would be legally binding on the Federal Republic of Yugoslavia.
Nato's control over the international force was one of the sticking points with the Serbian negotiators, and it could become one of the points of difficulty in coming days.
Mr Blair said Nato would continue bombing until a "full and verifiable withdrawal of all Serb forces from Kosovo had begun", with the threat of a Nato ground invasion force maintained to keep the pressure on President Milosevic .
"It is time Milosevic realised that the longer he tries to draw this out, the longer and harder his forces will be hit. We have only achieved this agreement by showing total resolve and determination.
"We shall need to be as resolved and determined now in implementing it. We did not and do not take Milosevic's assurances on trust. The Balkans are littered with his broken promises," Mr Blair added.
The Prime Minister also pledged that international aid for reconstruction work in Yugoslavia would not go ahead while "a nationalist dictator" remained in power in Belgrade.
"Until Milosevic goes, Serbia cannot take its true place in the family of world nations."
The Conservative Party leader, William Hague, welcomed the outline agreement as "very encouraging" and agreed that the "air campaign must not stop until there is a verifiable withdrawal of Serb forces".
The key test of the agreement, he said, would be its success in ensuring all the refugees returned to their homes in safety.
Donald Anderson, the Labour MP for Swansea East and chairman of the all- party Commons Foreign Affairs Committee, said: "It looks as if Kosovo will be seen as a famous victory for international order and international justice."
Paddy Ashdown, the Liberal Democrat leader, asked: "Isn't it true to say that it is not over until it is over on the ground in Kosovo?"
The Prime Minister agreed that Nato could not "take anything for granted until the killing actually stops on the ground".Reuse content