It comes less than a month after Mr Allen, the ex-commander of US and Nato forces in Afghanistan, was cleared by Pentagon investigators of allegations of professional misconduct over email exchanges with a Florida socialite.
The President said: "I met with General John Allen and accepted his request to retire from the military so he can address health issues within his family."
The decision by the Defence Department's Inspector General helped lift a cloud hanging over Mr Allen, who is married and has two daughters, since he became involved in the scandal that forced ex-General David Petraeus to resign as CIA director.
The Pentagon inquiry centered on emails between Mr Allen and Jill Kelley, who knew him when he served as the number two officer at the US military's Central Command from July 2008 to June 2011.
The Kelley-Allen emails surfaced when the FBI probed Kelley's allegations of receiving anonymous, harassing emails from someone else about Mr Petraeus.
Those emails led the FBI to uncover an affair between Mr Petraeus and his biographer, Paula Broadwell.