The deal is pending receipt of his international transfer certificate and visa.
The 23-year-old Leveron appeared in 20 games with the Honduran senior men's team and had nine goals in 83 appearances with club side C.D. Motagua. He also served as captain of the Honduran squad at the 2012 Summer Games in London .
"Johnny is a left-footed centre back who is very comfortable on the ball," Whitecaps head coach Martin Rennie said in a statement. "He's still young but he's captained the Honduran Olympic team and has already played a number of games for the senior national team.
"He has a very big upside and we are really excited to welcome him to Vancouver."