Detainee Transfer and Release Security Act of 2010 - Prohibits the President from releasing or transferring an individual currently detained at Naval Station, Guantanamo Bay, Cuba, to the custody of the individual's country of origin or to a third country unless the President certifies to Congress that: (1) such country is not a designated state sponsor of terrorism; (2) such country's government can secure and exercise control over all of its territory; (3) no portion of such country's territory serves as a safe haven for terrorists or insurgent groups, particularly al Qaeda; and (4) there is no confirmed case of any individual who had been detained at Guantanamo who reengaged in terrorist activities subsequent to being transferred or released to such country.