Ayew reunites with Forest manager Steve Cooper whom he worked with at Swansea City.
The 33-year-old is Nottingham Forest's 29th signing since gaining promotion to the Premier League last season.
Ayew has also previously played in England with West Ham United.
The former Olympique Marseille forward was a free agent after terminating his contract with Qatar side Al Sadd earlier this week.
Nottingham Forest are 13th on the Premier League table, four points above the relegation zone.
"It's a great feeling to sign for Nottingham Forest," said Ayew.
"I know how big the club is and I know how much the club means to the city and the fanbase. It's always been difficult whenever I've played against Forest and at The City Ground and I love the stadium.
"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."
"Steve Cooper is someone who knows me very well and knows how to work with me both on and off the pitch," added Ayew.
"We have a strong relationship, he's a special coach and a special human being and someone who I really look up to."
A veteran of three FIFA World Cups, Ayew has been capped 113 times by the Ghana national team.