He was born in Langley, British Columbia, Canada. His grandfather, Arne Tuft, was an Olympic cross-country skier from Norway.
Tuft dropped out of school at 15 to travel and camp with his dog named Bear. He spent the next several years mountain climbing and going on long bike trips, including a 4,000 mile trip to Alaska as a teenager.
While racing with the Symmetrics, Tuft lived in a trailer behind team owner Kevin Cunningham's house near Langley. In the adjacent trailer was Tuft's teammate Christian Meier. The team referred to the two as the trailer park boys.
Tuft first raced in 1999, at the British Columbia Provincial Championships. Strong results landed him a place on the Broadmark Capital team, followed by short stints on the Mercury and Prime Alliance teams. Tuft's career flourished when he rode for the Canadian Symmetrics team – a prominent team in North American Cycling from 2005–2008. He first captured the Canadian national time trial title in 2004 from his former teammate and three time Canadian Olympian Eric Wohlberg. Wohlberg held the title for eight consecutive years prior to Tuft. In 2007 Tuft conceded the Canadian National Time Trial title to Ryder Hesjedal.
He was selected to compete for Canada at the 2008 Summer Olympics in Beijing China in the Road Race and Time Trial. Svein Tuft was the best finisher for a long time in the time trial, before eventually finishing 7th.
His best result was second place in the 2008 UCI World Championships time trial in Varese Italy during which he overcame a flat tire in the last 5 km.
He featured prominently in a Symmetrics team Comic book written by Marvel Comics Dabel Brothers Productions Editor in chief Matthew Hansen, which is used as a press kit for the team. In the comic book, Tuft is very muscular. Upon seeing himself in the comic, Tuft remarked "We're all a bunch of sissies really."
In 2011 Svein Tuft was supposed to be a part of Team Pegasus Cycling. Unfortunately due to sponsorship issues, the team had to pull out at the last minute. Tuft was recruited as a member of the Canadian Professional Pro-Continental Team, SpiderTech–C10, managed by Steve Bauer. Tuft won both the Canadian National Time Trial and Canadian National Road championships in Burlington, Ontario with SpiderTech in 2011. In August 2011, Tuft announced that he would leave SpiderTech for the Australian team GreenEDGE in 2012.
He was praised for his 200 km solo ride in front of the peloton during stage 2 of the 2012 Tirreno–Adriatico. During the race, he reportedly burnt 6500 calories. Mark Cavendish tweeted it as "Ride of the day.. No, make that ride of the millennium, goes to GreenEDGE's Svein Tuft. 200km ALONE controlling the peloton! Respect."
In August 2012, Tuft prevailed on stage 6 of the Eneco Tour, a 17.4 kilometres (10.8 mi) Individual Time Trial. The victory put him in the overall classification leader's jersey. He lost the lead the next day on the seventh and last stage of the Tour, where he had to face the steep climbs of the Belgian "bergs." Tuft was announced as the third overall rider, but he was handed a 20 seconds penalty for taking a bottle of water from his team's car with less than 20 km (12 mi) to cover, which is against the rules. That punishment relegated him to seventh place, one minute behind winner Lars Boom of Rabobank.
In 2013, Tuft opened his account and took the first victory of the season for Orica–GreenEDGE, by winning the individual time trial in the Tour de San Luis. The 19.2 km (11.9 mi) course was swept by strong winds, according to Tuft. In July, he was the lanterne rouge – final-placed rider overall – of the 100th Tour de France.
In 2014, Tuft wore the maglia rosa as leader of the Giro d'Italia since Orica–GreenEDGE won the opening team time trial and he crossed the line first. He stated afterward: "For a guy like me, to wear the maglia rosa is a once in a lifetime experience, and I’m really thankful to my team for that gift. It’s a really special thing."
In 2015, Tuft crashed at the Tour de Romandie as he was carrying water bottles to give to his teammates. He was a non-starter for the third stage. It was later revealed after medical examination that he had suffered a minor wrist fracture and a sternum injury, and was therefore pulled out of Orica–GreenEDGE's Giro d'Italia's roster.