After Wigan's relegation from the second-tier EFL Championship last season, McClean, 34, has opted to drop down a further division to join Wrexham's campaign in League Two.
Friday's move represents a further statement of intent from Wrexham's celebrity owners Ryan Reynolds and Rob McElhenney as they seek to build on their promotion from the National League.
According to reports, Wrexham have paid a fee of £250,000 ($319,000) to pry McClean away from Wigan, where he was voted player of the year by supporters last season. He has signed a one-year contract at the Racecourse Ground, with an option of an extension.
"I'm really pleased with the signing of someone with the calibre of James," said Wrexham manager Phil Parkinson.
"As I said in the summer, it's about being patient and getting the players in who can be strong additions to our squad moving forward."
In a statement, Wigan said they were eager to keep McClean, who had 12 months left on his contract, but were unable to agree new terms.
In a career that has also seen him represent Sunderland, West Bromwich Albion and Stoke City, McClean has made over a 150 appearances in the Premier League and in June won his 100th cap for the Republic or Ireland.
"I'm absolutely delighted to sign for Wrexham. It's a project that is very exciting and I'm looking forward to being a part of it," McClean said.
"The Club has ambitions to go even further, and I'm a very ambitious person. I'm someone who is driven and I want to be a part of that journey."
Wrexham, who will be without injured forward Paul Mullin to start the season, will begin their League Two campaign at home to MK Dons on Saturday.