"Acting Secretary of Defense Patrick Shanahan, who has done a wonderful job, has decided not to go forward with his confirmation process so that he can devote more time to his family," Trump tweeted.
Shanahan appeared to downplay concerns about his candidacy last week.
"I can't tell you how long the process is supposed to work," Shanahan responded when asked why it is taking so long for his paperwork to be sent from the White House.
When asked last week if he had assurances from Trump that he was still the president's pick to lead the Defense Department, Shanahan said he is "in contact with the White House" and expects the process to be completed shortly.
"I'm in contact with the White House. We're done with our paperwork, expect to have the process completed here shortly," he said.
While Esper will replace Shanahan as acting defense secretary, Trump did not specify whether he will also become the new nominee to take on the role full-time.
Esper's name had previously been floated before Trump nominated Shanahan and his allies have been pushing for the president to nominate him over the acting secretary for weeks.
Asked about Esper's interest in the secretary of defense role, his spokesman pointed to a December statement in which the Army secretary told the Ft. Worth Star-Telegram: "I'm very happy and privileged to be secretary of the Army."