Turner departs Arsenal after a single season in which he served as backup to Aaron Ramsdale and made just seven appearances — all in cup competitions.
At Forest, who are preparing for their second season back to the Premier League, Turner should have an clearer path to the first team.
“It feels great to be here. It’s something I’m really looking forward to, it’s a great challenge and a great step in my career,” he told the club’s website.
“When I heard that there was interest to bring me here, it just felt right for my family, it felt right when my agent spoke to me about it and it feels like the right move for me right now.
“The manager and the backroom staff, everything about the club has a little sparkle to it. It’s felt right from the start and I’m happy it’s got done.
“I’m looking forward to making a connection with my teammates, the fans and the city. I’m grateful to be here and can’t wait to get things started.”
However, ESPN has reported that the Midlands club are also close to signing Dean Henderson from Manchester United. Henderson, an England international, spent last season on loan at Forest, making 18 Premier League appearances in goal.
Turner, 29, joined Arsenal from MLS side New England Revolution last summer but was unable to usurp Ramsdale as the club’s No. 1. In his seven appearances — five in the Europa League and two in the FA Cup — Turner kept four clean sheets.
Despite his lack of action at club level, Turner cemented his position as the first-choice goalkeeper for the USMNT. As well as starting all four games as the U.S. reached the round of 16 at the 2022 World Cup, Turner also featured in both the Concacaf Nations League and Gold Cup this summer.