The 24-year-old defender played in all three of his country's World Cup group matches in South Africa and took several long shots on goal in games against Portugal and Brazil.
His agent Karl Messerli told The Associated Press that Cha, who will be leaving North Korean state-owned club Amrokgang, will become the third North Korean to transfer to Switzerland in the past year.
"We have the work permit and he will arrive in two weeks," Messerli said.
"The aim is to prepare this player for the European leagues. Of course he won't play all his life in Wil. We want to test him, let him play, and prepare him for higher tasks."
Messerli said there will be no upfront transfer fee, but Amrokgang will be paid on results if Cha proves himself or is sold to a bigger team.
Wil already has 21-year-old North Korean midfielder Kim Kuk Jin, who joined the club last year.
A third player
Messerli said an English and a German club had expressed an interest in two more players from North Korea's national squad, which exited the World Cup after a group stage that included a 7-0 drubbing by Portugal.