The former assistant manager has been in interim charge since Sam Ricketts left to join Shrewsbury Town.
He said he wasn't interested in the role when he stepped in but was committed to working with the new manager whenever an appointment was made.
But the board have talked him round and he has signed a deal until 2021.
"We are delighted that Graham has accepted the offer to lead Wrexham AFC at an extremely exciting time in the development of the club," a statement read.
"Graham has impressed everyone since joining us in the summer and, along with the current backroom staff, has been a massive part of a great start to the season.
"He was the outstanding candidate to build on that work and hits the ground running after several impressive displays by the team under his guidance."
His first game in change as official manager will be this weekend's National League match at Aldershot.