The 22-year-old joined Zurich from Red Bull Salzburg last season and became an instant hit, scoring12 goals in 18 games.
"We have already agreed before our holidays, but we still had to wait until he got the official release," Canepa told his club's website.
"I do not comment on numbers. But we canceled the deal from England.
"I am concerned about the sporting aspect, we want to play the season with a powerful and ambitious troop and we see Raphael as a key part of that agenda," he added.
Dwamena made his debut for Ghana in June when the Black Stars thrashed Ethiopia 5-0 in the 2019 Africa Cup of Nations qualifiers in Kumasi.