"Despite continued questions that should be answered regarding the voting process, I personally believe that the majority of our citizens have spoken and we now should do everything we can to support the 75th governor of North Carolina, Roy Cooper," McCrory said in a video released Monday by his office.
In a statement, Cooper thanked the McCrorys for their service and said he looks "forward to working with them and their staff in what I expect will be a smooth transition."
Cooper won 49 percent of the vote, with McCrory close behind at 48.9 percent.
The North Carolina gubernatorial race was the last one in the nation without a winner called.
On Nov. 22, with McCrory trailing by about 6,500 votes, his campaign announced it would join Chuck Stuber, a candidate for state auditor, in filing for a statewide recount, when counties had yet to finish counting ballots.
"With many outstanding votes yet to be counted for the first time, legal challenges, ballot protests and voter fraud allegations, we must keep open the ability to allow the established recount process to ensure every legal vote is counted properly,” Russell Peck, McCrory's campaign manager, said in a statement.
Cooper's campaign manager, Trey Nix, responded to McCrory's request for a recount, saying in a statement, "We are confident that a recount will do nothing to change the fact that Roy Cooper has won this election."
McCrory came under fire earlier this year for signing the controversial House Bill 2, otherwise referred to as the bathroom bill.
Cooper, who is now North Carolina's outgoing attorney general, called House Bill 2 a "national embarrassment" and would not defend it. During the campaign, he argued that the bill should be repealed.
In exit polls from Election Day, 66 percent of North Carolina voters opposed the bathroom law, and 29 percent supported it.
ABC News' Geneva Sands, Gary Langer and Ryan Struyk contributed to this report.
Editor’s Note: A previous version of this story misreported the percent of those opposed to HB2 as 65 percent and from an exit poll from the North Carolina primaries.