The Mexican government also granted bids to an Argentine consortium and a US-Mexican consortium for smaller areas.
Eni, along with its Mexican partners, will exploit the Amoca, Mizton and Teocalli fields, which cover some 67 square kilometers (26 square miles) off the southeastern Mexican coast, Martin Alvarez with the National Hydrocarbons Commission said.
The fields are just 33 meters (108 feet) below the ocean surface and have a proven reserve of 107 million barrels of crude, Alvarez said.
Eni offered the Mexican government an 83.75-percent operational participation, far above the 34.8 percent that officials had set as a basis for bidders.
The Italian government has a 30-percent stake in Eni, making it the company's largest shareholder.
The Argentine consortium -- Pan American Energy, together with E&P Hidrocarburos y Servicios -- won a bid for a 40-square-kilometer underwater field at a depth of 82 meters, which has 93 million barrels of crude.
A third contract for the Ichakil and Pokoch fields was awarded to a group formed by the US-based Fieldwood Energy and Mexico's Petrobal, which offered the Mexican state a 74-percent stake in the operation.
Five production contracts in partnership with the Mexican government were put up for auction Wednesday, but only those three were granted.
Nine companies and five Mexican and foreign consortiums participated in the bidding.
Wednesday's auction was the second round for private investors following an auction held in July.
On July 15, Mexico put the development of 14 shallow-water Gulf of Mexico sites up for auction, but attracted only two bidders.
The most highly anticipated auctions are for deep-water sites, which will take place in early 2016.
Last year, President Enrique Pena Nieto approved controversial reforms to the petroleum sector, breaking up a state monopoly that had dated to 1938, with a goal of revitalizing oil production and stimulating the country's economy after years of declining production.