The deal is thought to be worth around £63 million in total including bonuses for Marmoush, who joins Pep Guardiola's ranks until June 2029.
"This is a day I will never forget," Marmoush said. "To sign for Manchester City - one of the best teams in the world - is an amazing feeling. I am delighted, my family are so proud, and we are all very happy to be here in Manchester.
"With Pep, his technical staff and the world-class facilities here, players have everything they need to improve. That was really enticing for me when I had the chance to come here."
A versatile forward, Marmoush can operate across the front line and leaves Frankfurt having scored 15 goals in the Bundesliga this season, which is just one behind Bayern Munich striker Harry Kane.
Marmoush joined Frankfurt on a free transfer from fellow Bundesliga side Wolfsburg in 2023, just 18 months ago.
"I cannot deny I also want to win trophies. City have been the most successful club in England for many, many years, so I know I am joining a winning environment and winning culture. I want to learn from the staff and my teammates, and I want to become a valued member of this winning team," Marmoush added.
"I really am looking forward to getting going, meeting the other players and showing the Manchester City fans what I can do."
Marmoush becomes City's third signing in January after defenders Vitor Reis, bought for £30 million from Brazilian side Palmeiras and Abdukodir Khusanov from Lens £34 million.
It takes City's spending beyond the £120 million mark this month as they seek to turn around an ailing campaign.
Guardiola's side are currently fourth in the Premier League but 12 points off top-placed Liverpool and are in danger of missing out on a play-off spot in the Champions League.