The National League club, via its Supporters Trust board, has revealed the identity of the duo after a special general meeting.
Canadian leading man Reynolds, 43, is famed for his title role in the Marvel smash hit Deadpool as well as several other extremely successful franchises.
His co-investor McElhenney, also 43, is an American actor, director, producer and screenwriter. He was the creative force behind comedy hit It’s Always Sunny in Philadelphia.
The outcome of the SGM revealed that 97.5 per cent of voters - 1,223 members - voted in favour of continuing with the takeover process.
Reynolds was revealed to be worth 71.5million dollars by Forbes earlier this year. McElhenney is worth 50million dollars.
In August, Vancouver-born Reynolds sold a gin business he co-owns for $610million.
In response to a tweet sent eight years ago saying 'you never know when Ryan Reynolds is going to turn up in Wrexham', the movie star replied saying 'Yes, you never know'.
The duo are poised to put forward their vision for the Racecourse Ground club in due course.
That will then be voted on by members at a second special general meeting.
Wrexham director Spencer Harris, who is also a director of the Supporters Trust, said: “It’s still at the stage where we have to finalise the deal and bring it back to the members at a second AGM.
“But I would like to think that Rob and Ryan think Wrexham is an attractive prospect with fantastic potential.
“People with the professionalism of Rob and Ryan do not come around very often and news of their interest is quite exciting for the supporters I’m sure.
“They are very driven individuals and very successful people in their industry.
“But from our discussions I can say they are both down to earth and want what is best for the club.”
He said contact had originally been made with representatives of the two actors before McElhenny and Reynolds had personally spoken to Wrexham officials.
“I’m sure people will consider it a remarkable story,” Harris said. “But I would ask for people to give us time to complete the story.
“Hopefully we can bring another amazing chapter to the history of what is the third oldest professional club in the world and the oldest professional club in Wales.”
Harris said he had spoken to the two Hollywood stars on a Zoom call on Wednesday night after the AGM backed the club to hold further investment talks.
The news comes with the National League season up in the air after the Government revealed fans would not be present for the start of the campaign.
National League bosses are meeting in the coming days to discuss how the season can play out with or without supporters.
Dean Keates' Wrexham fell to a 1-0 home friendly defeat to AFC Telford United, of the league below, last night. Shane Sutton headed in the winner from a Henry Cowans free-kick 16 minutes from time.