The announcement was made on Friday, three days after the resignation of acting Defense Secretary Patrick Shanahan.
The White House also said that the President will nominate Pentagon comptroller David Norquist to be Deputy Defense Secretary, and Army Undersecretary Ryan McCarthy to be Army Secretary, reported Xinhua news agency.
On Tuesday, Trump said on Twitter that Shanahan had withdrawn from consideration to be defense Szecretary, a post which requires Senate confirmation and has remained vacant for about six months since James Mattis resigned over policy disagreements with the White House.
Shanahan resigned due to allegations of violence surrounding his family.
"A painful and deeply personal family situation from long ago is being dredged up and painted in an incomplete and therefore misleading way" in the course of his confirmation process, Shanahan said in a statement, adding that he will also resign from his previous post as Deputy Defense Secretary and coordinate a transition plan.
Esper, 55, has acted as Secretary of the Army since 2017. His duties include the recruitment, organization, training, equipping, and care of 1.4 million active duty, National Guard, Reserve Soldiers, Department of the Army Civil and their families.
Before becoming Secretary, Esper, with a history of military service, once served as Vice President for government relations at Raytheon Company, a major defense contractor.
Espen, a West Point graduate and Gulf War veteran, is already set to become acting Defense Secretary though Shanahan's resignation will take effect on Sunday. However, federal law may force Shanahan to bow out of that post once Trump formally nominates Esper.
Trump would have to nominate Esper before July 30, because the act says a position can have an acting official for only 210 days, according to local media reports, noting that Mattis resigned effective January 1 this year.
( With inputs from IANS )