Jose Berardo, 61, who made a fortune in the mining sector in South Africa, had threatened to move his collection abroad if the government did not reach a decision by the end of the year to set up a museum to house it.
France, Japan and the United States had shown interest in housing the collection, which includes works by Roy Lichtenstein, Andy Warhol and Pablo Picasso.
Francis Bacon, Dan Flavin, Vito Acconci, the Chapman Brothers and Nan Goldin are also among the artists represented in his collection.
Art in Lisbon
Isabel Pires de Lima, Portugal's culture minister, said the collection would be housed at Lisbon's riverside Belem Cultural Centre, one of Portugal's main cultural venues. She did not say when it would go on display.
De Lima said: "It is of extreme importance to keep Berardo's collection in Portugal. We have very small international collections, especially those pertaining to the 20th century."
Earlier this year ArtNews, the US magazine, singled out the collection as one of the 100 best in the world.
Berardo, the chairman of holding company Metalgest, is estimated to have a fortune worth more than $600 million, making him the 10th-richest man in Portugal, according to newsweekly Focus.
He has sought an agreement with Lisbon to display his collection in Portugal for over seven years and had grown increasingly frustrated with the lack of progress in the talks.
In October the businessman met Philippe Douste-Blazy, the French foreign minister, and Renaud Donnedieu de Vabres, the French culture minister, in Paris to explore the possibility of moving his collection to France.
"It is of extreme importance to keep Berardo's collection in Portugal"
Isabel Pires de Lima,
Portugal's culture minister
Among the possible sites proposed by French officials to hold the collection was the Ile Seguin near Paris where Francois Pinault, a French billionaire, had planned to build a museum to house his contemporary art collection.
Pinault abandoned the project earlier this year because of administrative obstacles in getting government approval for it and decided instead to display his collection in Italy, sparking controversy in France.
In October, de Lima announced an agreement between Lisbon and the Hermitage Museum of St Petersburg under which Russia's bastion of art will set up a branch in Lisbon, the Portuguese capital, in 2010.