The order to withdraw American troops from Syria has been signed, the U.S. military said Sunday, following U.S. President Donald Trump's surprise announcement last week of the withdrawal.

No details were given on how and when the pullout of some 2,500 troops will take place.

"The execute order for Syria has been signed," a U.S. military spokesperson told AFP when asked about the withdrawal order, without providing further details.

Last Wednesday Trump announced that the U.S. would withdraw its troops from Syria, following an Oct. 14 phone call with President Recep Tayyip Erdoğan in which the two leaders agreed on the need for more effective coordination over the war-torn country.

The announcement reportedly took the Pentagon by surprise.

A day after Trump's announcement, Mattis resigned, saying that his views were not aligned with those of the president.

Congressman and former presidential candidate Ron Paul has praised the widely criticized pullout decision.

Speaking on CNN, Paul said Sunday: "I am very proud of the president. This is exactly what he promised, and I think the people agree with him. We've been at war too long and in too many places ... spent several trillion dollars on these wars everywhere."

Sharing Paul's remarks on Twitter, Trump thanked the congressman for his support.

The withdrawal announcement comes on the eve of a possible Turkish military operation in northeastern Syria against the PKK terrorist group affiliated People's Protection Units (YPG).

Since 2016, Ankara has successfully carried out two similar military operations in northern Syria.

Trump and President Recep Tayyip Erdoğan spoke by telephone on Sunday and "agreed to ensure coordination between their countries' military, diplomatic and other officials to avoid a power vacuum which could result following any abuse of the withdrawal and transition phase in Syria," the Turkish presidency said in a statement.

Late Sunday, Trump tweeted that Erdoğan had assured him that any remaining Daesh fighters in Syria will be eliminated.

U.S. troops will leave under the auspices of a new Pentagon chief set to start next month, after Jim Mattis resigned from the post citing key differences, including on Syria, with the often-impulsive Trump.

Trump's sudden decision sparked turmoil within his administration, prompting the resignation of Brett McGurk, the special envoy to the anti-Daesh coalition, as well as Mattis.

Plans for the troop withdrawal will now be overseen by Deputy Secretary of Defense Patrick Shanahan, who Trump on Sunday said would replace Mattis starting January 1.

Mattis, 68, had said he would leave at the end of February to allow a smooth transition for the next chief of the world's top military power -- but a reportedly angry Trump accelerated his departure by two months.

Defense spokeswoman Dana White tweeted that Mattis would still assist in the handover, working with Shanahan to ensure the department "remains focused on the defense of our nation during this transition."

According to U.S. media, Trump voiced resentment over news coverage of Mattis' stinging resignation letter that laid bare his fundamental disagreements with the president.

Days later, special envoy McGurk made a similar move, saying he could not support Trump's Syria decision that, he said, "left our coalition partners confused and our fighting partners bewildered."

Unlike Mattis, Shanahan has never served in the military and has spent most of his career in the private sector.

He spent over three decades working for aircraft giant Boeing, including as vice president and general manager of Boeing Missile Defense Systems, before moving to the Pentagon as a deputy in 2017.