The duo were among 14 players who have been released by Premier League returnees ahead of the 2022-23 season.
Fulham are expected to strengthen their squad by bringing in new and experienced players.
Ameyaw joined Fulham in September 2020 and was given a one-year contract last year, but he had a disappointing 2021-22 season, prompting the decision to release him.
Opoku has been at Fulham since 2017 but has yet to break into the first team. His development has been slowed, and the club believes it is best to release him.
He spent last season on loan at Danish club Vejle BK.
Opoku was born in England, while Ameyaw was born in the United States. Both are eligible to represent Ghana at any level.