A La Liga top scorer with both Villarreal and Atletico, the former Manchester United forward was voted best player at the World Cup finals in South Africa last year as Uruguay reached the last four.
"Farewells are always hard, because it has been four years plus the three at Villarreal and now... I will be leaving behind people's kindness, which I will never forget," Forlan said at a news conference in the Spanish capital.
"I am looking forward very much to rejuvenating myself, it's all new and it's where you find motivation because the challenges are greater.
"You don't often get a chance to go to Inter at the age of 32 and I hope I can live up to the expectations."
The Copa America winner's arrival at Inter is good news for coach Gian Piero Gasperini, who has lost forwards Samuel Eto'o and Goran Pandev to Russian side Anzhi Makhachkala and Napoli respectively.
The Italian club, who lost their domestic crown to local rivals AC Milan last season, said in a statement on their website later on Monday that Forlan had arrived in the city and would complete his move on Tuesday.
"I am here to continue winning with Inter," the club quoted him as telling journalists at Linate airport. "My goal is to play and score as much as possible for my new team."
STILL SHARP
Forlan helped Atletico to a Europa League triumph in the 2009/10 season, when they also reached the final of Spain's King's Cup.
His club form dipped last season and Atletico announced last week they had given him permission to negotiate a transfer.
However, he was as sharp as ever at international level as he helped Uruguay win the Copa America this year, scoring twice in their 3-0 final win over Paraguay.
"I am very happy to be here and to be able to play for a fantastic team like Inter," Forlan said. "It's a great opportunity for my career."
