"We believe that the conclusion of this agreement can both allow for confidence-building in respect of Iran's nuclear programme and represent a significant development in relations between Europe and Iran," Straw said in a written statement.
"It is essential now for the agreement to be implemented in full," Straw added.
In an deal with the EU's three biggest powers -- Britain, France and Germany -- late on Sunday, Iran agreed to freeze uranium enrichment-related activities to ease fears its fuel cycle work could be diverted to make an atomic bomb.
The United States claims Tehran is secretly developing nuclear weapons and wants the matter brought before the UN Security Council, which could impose punishing sanctions.
A UN atomic agency report obtained on Monday by AFP said it had no proof to date of a secret Iranian nuclear weapons program but could not yet conclude definitively that there was no covert activity.