Freuler became the club's 15th signing of the summer, with manager Cooper making no apologies for the high influx of players.
The deal was announced just hours after Forest won their first home game in the Premier League since 1999 as they powered to a 1-0 success against West Ham.
The Switzerland international joins from Serie A side Atalanta and follows the Saturday arrivals of club-record signing Emmanuel Dennis from Watford and Cheikhou Kouyate on a free transfer.
Freuler, 30, has played 46 times for Switzerland, including at the World Cup and Euro 2020.
Forest are not expected to be done there having been linked with moves for Neal Maupay and Houssem Aouar.
Boss Cooper said there is a method behind the high turnover at the club this summer.
"I really hope everyone is looking into why we've had to make so many signings and not just put the narrative of 'Forest have signed loads of players, why?'" he said.
"There's been a real rationale behind it and it's been a real necessity. We have had no choice. We would have loved to carry on last year with our team and added a few players but it was never going to happen.
"We are still in that process of becoming that team and squad we want to be. We have a couple of weeks left of the window so there will definitely be ins and outs."