Thohir, who is part owner of Major League Soccer club DC United and basketball team the Philadelphia 76ers, heads a three-person consortium taking control of the former Italian champions.
Italian media have previously said Thohir might be willing to pay up to 350 million euros ($476 million) for up to 75 percent of the cash-strapped Serie A club.
"Everything's been signed," Moratti told reporters outside his offices in Milan, without giving any details on the price.
Inter, a loss-making club with debts of about 300 million euros, are traditionally one of the three biggest clubs in Italian soccer with champions Juventus and city rivals AC Milan.
They have not won a trophy since 2010 and finished a disappointing ninth last season, missing out on a place in the lucrative Champions League.
Inter stand fourth in the Italian league in the early stages of the current season.
Moratti, who has been in charge of Inter since 1995, said he was not sure if he would stay on as club president under the new ownership.
"If I can be useful I will continue," he said.
His father Angelo Moratti owned the club in the 1960s when Inter won the European Cup twice in successive years.
Italian football has not attracted the major foreign investment seen in countries like England and France.
Europe's top league in the 1990s, Italy's Serie A has been tarnished by a series of corruption scandals and hooliganism has reduced crowd numbers.
Italian clubs have been held back commercially because many of them do not own their stadiums and have been unable to upgrade them to cater fully for wealthy corporate clients.
Inter, for example, share the San Siro stadium with AC Milan and the ground is owned by the local authorities.
- Sports & Recreation
- AC Milan
- Major League Soccer
- Angelo Moratti