The 25-year-old full back, who recently left Championship side, Birmingham City, has put pen to paper on a two-year contract at Prenton Park.
Cogley, who has played a number of games in the second tier of English football, has also spent time on loan in League Two, at Crawley Town.
Manager Micky Mellon said: “I am delighted we have signed Josh. He is a real quality player, and he is someone we have been chasing since I came back in.
“We need the types of full backs Josh is if we are going to be able to play the way that we want to play. He is quick, mobile and aggressive. Josh has the desire to want to keep on improving and he is a really good signing for us.
“Josh made it clear he wants to come and play for Tranmere. He knows he demands of being a Tranmere Rovers player and the expectations that will be on him.
“Josh fits into what we want to do. We do not want to rush our recruitment; it takes time, and we are working hard for the players we want.”
Cogley added: “I am absolutely buzzing. I can’t wait to get started at Tranmere Rovers and I am ready to kick on.
“It is a new challenge and opportunity. I have learned a lot from the years I have been at Birmingham City even when I was a young training with the first team.
“I had a great chat with the manager, and he talked me through the plans, and what he wanted for the Club. He explained what he wanted from me, and I really liked what he had to say. I want to help this Club win promotion out of this league.”
Josh is available to sponsor ahead of the 2021/22 season. For further information on the player sponsorship packages available, please email debbieq@tranmererovers.co.uk.