Stankovic has looked set to leave for much of the season, despite coach Roberto Mancini's statement last summer that the Serb was intransferable.
However, the deeply indebted club have finally decided to sell the midfielder receiving cash and a half ownership of Goran Pandev - currently on loan at Ancona.
"We have lost a really big player," admitted Mancini on Saturday.
"I was convinced he could stay but I am merely the coach and the club makes the decisions.
"I could do nothing about it but now we have to look forward.
"Nothing has changed. We still have a strong team and we have to push on."
Stankovic - who would have been out of contract in the summer - has sealed a deal until 2008, and was delighted with his move.
"I thank Inter for the faith and patience they have shown," Stankovic told his new club's official website.
"I have nothing but respect for Lazio, who gave me the chance to play in Italy at the highest levels.
"Because of this I gave up part of my signing fee to allow Lazio to take more of the pot, bearing in mind my contract expired in June.
"Now I am starting a new adventure, in a big team at a big club.
"I now want to put myself at the disposal of my new team and the coach."
