The White House listed the planned nominations Friday.
Earlier this week Esper was designated as acting defense secretary, effective Sunday.
Trump described Esper as "outstanding" in comments to reporters Tuesday.
He is a "highly respected gentleman with a great career -- West Point, Harvard, a tremendous talent," Trump added.
Esper is set to become acting defense secretary after the resignation earlier this week of Patrick Shanahan, who previously worked as Mattis' deputy. Shanahan said he withdrew his name from consideration for the role to protect his children from focus on an F.B.I. investigation into a violent domestic dispute between him and his former wife nine years ago. The probe stemmed from a background investigation related to him possibly being considered as a nominee.
Esper is a former West Point classmate of Secretary of State Mike Pompeo. He previously served as vice president of government relations at the defense contractor, Raytheon. Before that, he served as an Army infantryman in the Persian Gulf War. He also served on active duty in Europe and on the Army staff in Washington before transitioning to the National Guard and retiring after 21 years of service.
He had served as an airborne ranger, and received the Legion of Merit, Bronze Star, and other awards.
The president nominated Ryan McCarthy, the under secretary of the Army, of Illinois, to replace Esper as secretary of the Army. He also nominated David Norquist, the Pentagon's Chief Financial Officer, also of Virginia, to be deputy defense secretary.