The Greek champions have secured the 22-year-old on a three-year contract for an undisclosed fee following Fulham's relegation from the Premier League.
Kasami made 35 appearances for Fulham last season and scored one of the goals of the campaign in their 4-1 win over Crystal Palace in October.
The Switzerland international missed out on a place in Ottmar Hitzfeld's FIFA World Cup squad but his displays did bring him to the attention of Michel, who will lead Olympiacos into the UEFA Champions League in the forthcoming season.
"I am very happy to have signed my contract and I'm very proud to be an Olympiacos player," he told the club's official website.
"I am very proud that I am now an Olympiacos player and I hope to offer great joys. I hope to win many titles, and cannot wait to play and score.
"Olympiacos are already playing in the UEFA Champions League against big teams. Everything is good, I like the whole team, I am looking forward to it."
Kasami becomes the second player in five days to make the move to Athens after Eric Abidal's switch from Monaco was announced on Saturday.
