The 21-year-old scored eight goals in 33 league appearances for the Gialloblu after leaving Lyon last summer, and negotiations over a move to San Siro began shortly after the 2012-13 season drew to a close.
Belfodil's arrival in Milan follows the permanent transfer of 30-year-old striker Antonio Cassano to Parma, although neither club emphasised the existence of a player-exchange deal.
A statement published on inter.it read: "Ishak Belfodil is an Inter player. The Algerian striker, a naturalised Frenchman, has been signed from Parma in a co-ownership agreement.
"He has signed a five-year contract which ties him to Inter until 2018."
The Algeria-born forward told his new club's official website: "Inter is a great club. I'm very happy to be here and I hope to do well here. A big hello to all the Nerazzurri fans!"
A part of Lyon's youth team since 2008, Belfodil spent six months on loan with Parma's local rivals Bologna before joining the Ducale club for 2.5 million euros in June 2012.
Having represented France at youth level since the age of 16, he received a first call-up to Algeria duty in August 2012 but was unable to play due to a FIFA processing error. His clearance would arrive a month later but he is yet to feature for Vahid Halilhodzic's side.
Inter later announced Argentinian goalkeeper Juan Pablo Carrizo had extended
his contract until June 30, 2015.
The 29-year-old former River Plate keeper arrived from Lazio in January and
made one league appearance for Inter in a 1-0 home defeat to Bologna.