Windass left Sheffield Wednesday after his contract was terminated by mutual consent with the Owls struggling to meet their wage bill.
He has now moved to Championship rivals Wrexham in a free transfer.
Windass, 31, said: "I'm looking forward to getting going. I've spoken to the manager, who has showed me his plans for the season and what he expects from the group, and I've really bought into that.
"I'd describe myself as honest and hard-working, I like to contribute goals and assists from midfield and that's what I'm looking to bring to Wrexham.
"First and foremost, I want to get into the team and earn the respect of my team-mates – I want to be professional, be someone to look up to and then get the team as high up the league as possible."
Wrexham manager Phil Parkinson said: "I'm delighted to welcome Josh to the club. He's a player with a lot of Championship experience and I'm looking forward to working with him over the coming seasons."