The announcement comes amid a staff shakeup in the Trump administration as the president seeks to enforce a tougher immigration policy at the southern border.
In April, Trump pulled Ronald D. Vitiello as his nominee for ICE chief, saying he wanted the agency to go in a "tougher direction."
Morgan served as the head of Border Patrol for the last six months of the Obama administration. He was removed from that post when the Trump administration took office.
Morgan has publicly endorsed Trump's call for a border wall and his decision to declare a national emergency at the border.
"The president had no choice, Congress has failed, they continue to fail," Morgan said in a February interview with CNN.
The change at ICE is only the latest staff shakeup involving immigration policy. Kirstjen Nielsen stepped down as the secretary of Homeland Security in April amid reports that Trump believed she did not do enough to secure the nation's southern border.
She was replaced by Kevin McAleenan, who previously served as the Customs and Border Protection commissioner.