The fee is undisclosed but many sources have quoted it to be between £300,000 and £500,000.
Wright looks set to replace Eaden as the Latics number one right back.
When asked about signing, Wright said: "I'm delighted to complete my move here and can't wait for training to start on Thursday now to be honest."
"The deal has taken a little time to complete but once I knew Wigan were definitely interested and that Crewe had accepted a bid, it wasn't a difficult decision to make.
"I had a great time at Crewe but I feel that the time is right to move on and I'm very excited to sign here at The JJB.
"It's the first move of my career and that makes it even more exciting as it should give my career fresh impetus."