Inter will play Leicester City, Crystal Palace, Norwich City and Portsmouth during their tour.
The club had issued a statement saying that they had no wish to add to the stress on police and security services by playing in London.
Furious Crystal Palace chairman Simon Jordan accused the club of cowardice during an interview with Sky Sports on Saturday afternoon.
He had vowed to sue Milan who, he said, had agreed to play the game – which celebrates Palace’s centenary as well as being a key part of their build-up to the new season - as part of a transfer deal which saw usually injured striker Nicola Ventola and defender Gonzalo Sorondo play for Palace in the Premier League last season.
Jordan pointed out that if England could play Australia in the first Ashes test in central London, he believed that Inter should be happy to travel to suburban SE25.
"I can officially confirm the tour is on as scheduled," Italy's ambassador to Britain told Reuters on Sunday.
"The team is leaving for the UK," Giancarlo Aragona said.
The cancellation of the tour had also drawn heavy criticism from London's mayor Ken Livingstone, who said such a decision played into the hands of the terrorists.
