Moratti had been in talks with Indonesian businessman Erick Thohir over a possible agreement for some time, and revealed on Tuesday the sale has now been finalised.
"It was all signed, I believe there will be a press release in a few hours," Moratti said following a meeting in Milan.
Moratti became Inter president in 1995 taking over from Ernesto Pellegrini, and sought to improve the team's fortunes on the field after they finished just one point outside the relegation zone in 1994.
Perhaps Moratti's proudest achievement was when Inter completed a historic treble in 2010, when Jose Mourinho led the club to the UEFA Champions League and Coppa Italia, as well as league success.
A ninth-placed finish last season saw Andrea Stramaccioni lose his job.
