Surachai Thansitpong, permanent secretary of the Transport Ministry and chairman of the airline, said the resignation would be effective from January 1.
Cabinet sources said one of the major disagreements with the board was Apinan's opposition to changes to the terms of a leasing package for eight new A330-300 jetliners to be procured by THAI.
On June 19, the Cabinet decided that the aircraft should be acquired by the "operating lease" method, instead of through "financial leasing".
According to the Transport Ministry, financial leasing would be more beneficial to the airline than operating leases as it would give the carrier flexibility when it comes to selling or scrapping the aircraft.
On the other hand, operating leases do not allow this, even though the aircraft are considered part of its assets.
Surachai said ACM Narongsak Sangkapong, a senior executive, had been named as acting president following Apinan's resignation.
"The board approved the resignation unanimously and the move had nothing to do with political intervention," he said.
Airline sources said Apinan is being investigated for alleged corruption in arranging overseas hotel accommodation for THAI staff. As a result, he had been under pressure to resign from the top management post.
Earlier, Apinan was suspended from active duty when Chaisawad Kittipornpaibul was chairman of THAI, but he was quickly reinstated.
Meanwhile, Transport Minister Santi Prompat denied there was any political pressure for Apinan to quit after a THAI pilot refused to fly his aircraft with a government MP on board during previous anti-government rallies.
"Please don't say that he's decided to quit to avoid further investigation into alleged corruption," said the minister, adding that the resignation was unlikely to impact the carrier's operations.
Chamsri Sukchokerat, chairwoman of the THAI labour union, said union members had accepted Apinan's decision and there would be no protest.
Apinan was appointed president in May 2006.