The release of the 15 captured British personnel will come as a "profound relief" to their families, Prime Minister Tony Blair has said.
He said the loved ones of the sailors and marines held by Iran had endured "distress and anxiety".
And the premier stressed Britain had taken a "firm but calm" approach to dealing with the Tehran regime.
Speaking in Downing Street, Mr Blair said: "I'm glad that our 15 service personnel have been released. I know their release will come as a profound relief not just to them but to their families who have endured such distress and anxiety.
"Throughout we have taken a measured approach - firm but calm, not negotiating, but not confronting either."
Mr Blair said: "I would like to thank our allies in Europe, our allies in the UN security council, for their support and also our friends and allies in the region who played their part.
"We're grateful to all of them, as we are to the officials in the Foreign Office and the Ministry of Defence and here in Downing Street for the work that they have done."
Mr Blair added: "To the Iranian people I would simply say this: we bear you no ill will. On the contrary, we respect Iran as an ancient civilisation, as a nation with a proud and dignified history.
"The disagreements that we have with your government, we wish to resolve peacefully, through dialogue. I hope, as I have always hoped, that in the future we are about to do so."
