Marine Corps Commandant Gen James Amos said he has appointed Lt Gen Thomas Waldhauser, commander of Marine Corps Forces Central Command, for the investigation.
He has been officially designated as the "consolidated disposition authority" for the allegations surrounding the video.
That designation places authority in one commander to initiate any necessary investigations and take any administration or disciplinary action that results from those investigations, officials said.
This investigation will be conducted in coordination with the ongoing Naval Criminal Investigative Service investigation into the incident, marine officials said.
The video, which appeared on the Internet this week, has been widely condemned by the top US leadership including Secretary of State Hillary Clinton and Defence Secretary Leon Panetta.