Former Wales international Robinson had been assistant at the club prior to Martin Rennie's departure in October.
Vancouver finished seventh in the Western Conference standings last season and Robinson, who arrived at the club in 2012 after a stint with the New York Red Bulls, is confident his charges can prosper under him.
"I have thoroughly enjoyed my first two seasons in Vancouver, and am looking forward to the start of the 2014 season - the club's 40th anniversary," he said in a statement on Vancouver's official website.
"We have an exceptional fan base, a solid core of youth and experience, and a committed ownership group. I'm really excited about the opportunity to drive this club forward."
Robinson will become the club's 15th coach, with club president Bob Lenarduzzi backing the 37-year-old to be a success at the BC Place Stadium.
"During his time with the club, Carl has shown the qualities you look for in a successful head coach - a strong leader, great communicator with both youth and experienced players, high soccer IQ, technical and tactical intelligence, and a great work ethic," he said.
"We are confident that Carl is a coach who will bring out the best in his players and help our club achieve success this season and beyond."
