Thohir is also a co-owner of Washington-based Major League Soccer team DC United and basketball’s Philadelphia 76ers.
Inter did not disclose how much Thohir had paid for a controlling share in the 18-time Serie A champions, but Italian media reported the price could be around €327m (£276m). That would value Inter at €467m (£395m).
Current owner Massimo Moratti said he could stay on as president.
Inter are ranked the 12th richest club in the world, according to Deloitte’s Football Money League, however they have debts totalling more than €200m (£169m).
Glazer Family: Owners of Man Utd and NFL’s Tampa Bay Buccaneers
Fenway Sports Group: Portfolio includes Liverpool and baseball’s Boston Red Sox
Stan Kroenke: Arsenal majority shareholder also owns Denver Nuggets in the NBA, NFL side St Louis Rams and Colorado Avalanche in the NHL
Shad Khan: Jacksonville Jaguars owner bought Fulham this year