"I want to give a really special thanks to my friend and new partner Massimo Moratti for his confidence and support and I also want to thank my associates Rosan and Handy, who I have known for more than 20 years," Thohir said.
Moratti will have no role on the board but has been confirmed as honorary president, while his son Angelomario has been named as vice president, alongside Soetedjo.
"I am very happy to have found the new owner of this glorious club," Moratti said. "I am certain that they are more than prepared to continue bringing success to these beloved colors.
"Personally I am honored to have been president of Inter for so many years."
Moratti took over the presidency when he bought the club in 1995. During his time in charge, Inter won five consecutive Serie A titles and also won the Champions League and Italian Cup in 2010.
The 68-year-old Moratti's last game as president was Inter's 2-0 victory over Livorno.
Thohir is also part owner of the Philadelphia 76ers and D.C. United. He is chairman of the Mahaka Group, which has business interests in media and entertainment.
Inter's last trophy was the 2011 Italian Cup. The team is currently fourth in the Italian league, seven points behind leader Rome the only other Serie A club to have foreign owners.
Roma, which has yet to lose a game this season and won a record 10 matches to open the season, was taken over by a group of Boston executives in 2011.