"I have just been notified that two separate complaints have formally been made against me… I am, therefore, writing to request that you commission an independent investigation into the claims as soon as possible," Raab said in a letter to the prime minister.
Raab promised to "cooperate fully" and accept any results of the investigation, noting that he will continue to serve the government with "professionalism and integrity."
Sunak has approved the request of his deputy, adding that this was "the right course of action."
On Monday, Simon McDonald, a former Foreign Office senior civil servant, told reporters that Raab was so rude to his employees during his term as foreign minister that people were "scared to go into his office."
On November 11, 15 employees of the Ministry of Justice were reportedly offered "respite or a route out" after Raab's reappointment, due to concerns over possible damage to their mental health.