Flares were lit in celebration and people were singing and dancing after goalkeeper Gianluigi Donnarumma had saved the final kick.
Many fans had gathered in front of the Colloseum and at the Piazza del Populo in Rome to watch the game on big screens.
A government statement said that Draghi wanted to to thank the team, coach Roberto Mancini and his staff.
It said the team had shown “an extraordinary game and a special team spirit in addition to great individuality.”
The Italian team which are now undefeated in 34 matches were to return home from London during the night.(dpa/NAN)