The deal will give the 104-year-old club a new stadium to be built by China Railway Construction Corp, the main partner in the first such investment from mainland China in a major foreign sports team.
Asian sports marketing company QLS will take a token stake, one of the sources said.
"F.C. Internazionale welcomes the new shareholders," Inter said in a statement, without identifying the Chinese investors.
Inter Milan did not give any financial details of the deal. China Railway will build the new stadium by 2017, Inter said.
One of the sources familiar with the situation said the deal envisages more Asian investors eventually taking stakes in Inter, even though the Moratti family will retain majority control.
"The main aim is to build a new stadium, that's what the agreement with China Railway is really about," Massimo Moratti, chairman and owner of Inter, said.
Chinese investors, encouraged by the government, have been actively pursuing overseas assets in recent years. Some high-profile purchases have included the takeover of cereal maker Weetabix by China Bright Food and an agreement by Dalian Wanda Group to buy the U.S. movie chain AMC Theatres, both in May.
Inter and arch-rivals AC Milan, owned by former Italian Prime Minister Silvio Berlusconi, use the existing San Siro Stadium, which is owned by the city of Milan and has a 80,065 capacity.
A spokeswoman for Milan city council said there was no decision yet on where the new Inter Milan stadium could be built. Any decision would need to go through Italy's lengthy authorisation process.
Rival Italian club Juventus recently built their 41,000-seater stadium in Turin.
China Railway Construction has actively pursued overseas investment this year, signing two projects in Africa with a total contract value of £1.1 billion. In November last year, a consortium involving the Shanghai-listed company announced a deal to develop an iron ore mine in Guinea.
Investors from the Chinese mainland have been pursuing stakes in foreign sports teams, but with little success previously.
The Los Angeles Times reported last year that the Dodgers had received a £950,000m offer to buy the city's troubled Major League Baseball team, funded, in part, by Chinese investors.
Chinese investors launched an attempt to buy the Cleveland Cavaliers basketball team in 2009, Thomson Reuters data showed, and in 2010, news reports said investors from China bid for the Liverpool football club.
In 2009, Hong Kong businessman Carson Yeung bought English club Birmingham City.