The 69-year-old was formerly president of the club before selling his majority share to Indonesian businessman Erick Thohir in October last year.
Under Moratti, Inter won five Serie A titles as well as one UEFA Champions League crown, with the Italian overseeing the signings of players including Ronaldo and Luis Figo.
However, he will now step down from his honorary role with son Angelomario also leaving his post as a director.
"Internazionale Holding Srl, a company headed by Massimo Moratti and his sons Angelomario Moratti and Giovanni Moratti, and holds 29.5 per cent of FC Internazionale Milano Spa communicates that today Angelomario Moratti, Rinaldo Ghelfi and Alberto Manzonetto have each individually resigned their posts as director at Fc Internazionale Milano Spa," read an Inter statement.
"Internazionale Holding Srl also announces that Massimo Moratti has today resigned as honorary President of Fc Internazionale Milano Spa kindly offered to him by Erick Thohir in November last year."
Speaking to Mediaset Premium prior to Inter's UEFA Europa League draw with Saint-Etienne on Thursday, Thohir said: "I respect Mr Moratti's decision. I met him and we had a discussion.
"The relations between the two families won't change. He wants to support me and I think the media can ask him. At the same time, as the president I think I have to review some of the operations at the club."
Moratti was in the headlines this week after comments regarding current coach Walter Mazzarri as he failed to back Mazzarri's position at San Siro.
"Don't take me as an example, I sacked a coach two days after winning the league," Moratti told reporters, citing the example of replacing Roberto Mancini with Jose Mourinho in 2008.