Spalletti led AS Roma to second place in Serie A this season but left last week after deciding not to renew his contract.
Since then, he had been widely expected to take over at Inter Milan, who finished the season under interim coach Stefano Vecchi.
"It's all done because we've shaken hands," he told reporters at Milan airport. "I'm one of those old fashioned types who does things with a shake of the hand. I'm happy to be the new coach of Inter."
Inter have been under Chinese ownership since June last year when electronics retailer Suning Commerce Group Co Ltd bought a nearly 70 percent share for 270 million euros (£235.3 million).
However, they have had a turbulent first year.
Roberto Mancini resigned two weeks before the start of last season and was replaced by Frank de Boer, who himself was sacked after 85 days. His replacement, Stefano Pioli, was himself fired last month after a seven-match winless run.
There was no official comment from the club on Tuesday.
(Reporting by Brian Homewood; editing by Mark Heinrich)
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