Tzuberi's first achievement was a silver medal in the 2000 Windsurfing World Championships for boys. With the Olympics in mind, Tzuberi began mastering the Mistral windsurfer (which was the windsurfer model used in the Olympic Games at the time). In 2002, Tzuberi won the under-17 World Championships, and in 2004, he won the silver medal in the Youth World Championships held in Bulgaria.
In 2004, the ISAF decided to replace the Olympic windsurfing discipline model from the Mistral surfboard to the "Neil Pryde" RS:X surfboard. The majority of Olympic windsurfers found it hard to adjust to the new model, as they were already used to years of sailing on the Mistral. However, this provided younger surfers, such as Tzuberi, with a chance to close the gaps in experience and catch up with the veteran windsurfers.
Shahar Tzuberi was born in Eilat, Israel, to a family of both Yemenite Jewish and Ashkenazi descent. He began surfing at the age of 7, encouraged by his father, Ze'ev "Poodle" Tzuberi. After winning a number of local surfing competitions, he began training professionally. Tzuberi joined the Israel Defense Forces in 2005 and received an "Athlete of Excellence" status, allowing him to compete in international competitions. He went through recruit training in the Zikim base and then became a quartermaster in the Israeli navy base in Eilat, his hometown. His cousin is Israeli Surfer Hadar Heller.
Tuber competed for Israel at the 2008 Olympics, and entered the 2008 Olympic Games under the Shadow of Gal Fridman, a two-time Olympic medalist for Israel. He was ranked outside the top 10 coming into the tournament, but upgraded to an overall 1st place after the first 4 (of the total 11) events, finishing 1st and 3rd respectively. In the following 4 events, Tzuberi's best finish was a 6th place, in between 17th, 18th and 19th-place finishes – results that seemed to end his hopes of an Olympic medal. He then won the 9th and placed 4th in the 10th event, thus re-entering the medal race as 4th place overall.
Competing for Israel at the 2012 Olympics in windsurfing, he came in 19th.
Tzuberi had to place 4 places ahead of one of the top-3 surfers in order to win a medal and he accomplished just that by coming back from last place and finishing in an incredible 2nd place, and 3rd overall, while Great Britain's Nick Dempsey lost his medal by placing 7th – an overall 4th-place finish.
Tzuberi competed for Israel at the 2016 Olympics, his third appearance in the Olympic Games. He did not qualify for the finals.
