The resignation of the Channel 9 broadcaster president will take effect on June 12, the source said.
Mr Anek took up the position of Mcot president in October 2012, moving from secretary-general of the Office of the Education Council. A selection panel said during the selection process that he had administrative vision and knowledge of digital television broadcasting.
It had been speculated recently that he would leave, but Mr Anek had denied it.
The source said Mcot staff were opposing a push for Pathrlap Davivongsa, an independent director, to be the interim president after Mr Anek steps down while the company searches for his successor.
The staff demanded a professional executive be selected to run the company and political interference be ended, according to the source.
Mr Pathrlap is believed to have close ties with Yaowapa Wongsawat, a sister of former prime minister Thaksin Shinawatra.