The 24-year-old, who played for Japan at the World Cup in Brazil, will be given a formal send-off by Cerezo after next Tuesday's J-League game at home
to Kawasaki Frontale, officials added on the club's website.
"After the disappointment of the World Cup I've been thinking (about my future)," Kakitani said in a statement, referring to Japan's meek World Cup exit.
"I've been offered the chance to move to Europe so I've decided to take the challenge and move to Basel."
Basel have won the Swiss Super League for the past five years and did the double over Chelsea in the group stages of the European Champions League, although they failed to progress to the knockout round.
Japan crashed out of the World Cup in the first round after losing 2-1 to Ivory Coast, drawing 0-0 with 10-man Greece and being thumped 4-1 by Colombia.