The Ghana captain, a free agent, arrives from Qatari side Al-Sadd, where he played since 2021, scoring 15 goals in 21 league matches and winning the Qatar Stars League title last season.
Ayew returns to Britain where he had spells at Swansea City and West Ham United and will again be coached by Steve Cooper, who he worked under at the Welsh club in 2019.
"It’s a great feeling to sign for Nottingham Forest," said Ayew. "Steve Cooper is someone who knows me very well and knows how to work with me both on and off the pitch.
"I know what I can bring to the team, I’m ready to give my all and make sure that we are able to stay in the Premier League."
Ayew has 113 caps and has been to three World Cups, including last year's edition in Qatar.
Nottingham Forest are 13th with 21 points, four points above the relegation zone, and host Leeds United, who are two places and three points below the Midlands side, on Sunday.
