The 70-year-old, once the world's richest man, was suspended from the body last week pending an inquiry by the organisation's Ethics Commission.
Tsutsumi was arrested in his homeland last month on suspicion of fraud and insider trading after it was revealed that his Seibu Railway company had submitted false reports on its ownership structure for decades.
The IOC said Tsutsumi had written to their Lausanne headquarters informing them of his decision.
The IOC accepted Tsutsumi's decision and said that ends the procedure before the Ethics Commission.
Tsutsumi had been instrumental in bringing the 1998 Winter Olympics to Nagano, Japan, and was appointed to his IOC role in 2000.
Honour members can attend IOC meetings but do not have voting rights. Tsutsumi had been one of only four honour members, a list that also includes former U.S. Secretary of State Henry Kissinger.