"It is a sign of the regard that people have for Britain and Baroness Ashton that we have secured this important position for the country," he told reporters in Brussels.
In her new role, Baroness Ashton said she was pursue a policy of "quiet diplomacy", representing EU values around the world and "forming the relationships we must have" to ensure Europe continued to exert influence.
Baroness Ashton emerged as a surprise candidate for the role on Thursday, when the EU's 27 leaders also announced that Belgian Prime Minister Herman Van Rompuy would become the president of the EU Council - the job for which Mr Blair had been a prime candidate.
The BBC's Dominic Hughes said there had been unanimous backing for Baroness Ashton once her name was put forward for the role by the UK.
With Mr Van Rompuy representing the centre-right Christian Democrat bloc, EU leaders are thought to have wanted to give the foreign affairs portfolio to a centre-left politician as a counter-balance.
European Commission president Jose Manuel Barroso said her appointment showed the UK remained at "the heart of our project".
The Tories said Baroness Ashton's appointment demonstrated Gordon Brown's determination to "have someone in one of those roles".
"I think we have missed an opportunity here," said Timothy Kirkhope, the leader of Tory MEPs in Brussels.
"I wonder whether being the high representative for foreign affairs, when there are a lot of foreign policies in different capital cities around Europe, whether that has actually missed out for us in getting more influence in the area of economics."
Baroness Ashton was a government minister for eight years, latterly as leader of the House of Lords, before being chosen to replace Lord Mandelson as EU Trade Commissioner in 2008.
She is not a well-known figure in British politics but has been commended for the job she has done in her current role.
British Foreign Secretary David Miliband was heavily linked to the role of foreign affairs chief, created under the terms of the Lisbon Treaty.
However, he said he wanted to stay in British politics.
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