Bure was around nine years old when his parents separated. In 1991, he joined his father and brother, Pavel in moving to North America as his elder sibling embarked on a National Hockey League (NHL) career with the Vancouver Canucks. His mother arrived two months later. They settled initially in Los Angeles where Vladimir continued to train and coach both Valeri and Pavel in hockey and physical conditioning. However both became estranged from their father, along with his second wife and their half-sister Katya, by 1998. Neither brother has explained a reason for the split.

Upon turning professional in 1994–95, Bure spent the majority of the season with Montreal’s American Hockey League (AHL) affiliate, the Fredericton Canadiens. He had 23 goals and 48 points in 45 games for the club. Bure earned a recall to Montreal late in the season and made his NHL debut on February 28, 1995, against the New York Islanders. His first goal came two weeks later, on March 15, against goaltender Wendell Young of the Pittsburgh Penguins. In 24 games with Montreal, Bure scored 3 goals and added an assist. Playing in his brother’s shadow – Pavel had become a superstar in Vancouver – Valeri struggled to live up to the expectations placed on him. He scored 22 goals and 42 points in his first full season in Montreal, 1995–96, but scored only 14 goals the following season. He battled injuries that season; two concussions and a kidney injury limited him to 64 games, 13 fewer than the previous season.

After appearing in one game at the inaugural World Cup of Hockey in 1996, Bure played in his first of two Olympic Games in 1998. The tournament marked the first time he played with his brother Pavel since they were briefly teammates with CSKA Moscow in 1991. Valeri scored one goal in the tournament, and Russia advanced to the gold medal game. They settled for the silver medal after being shut out by Dominik Hašek and the Czech Republic. Bure returned for the 2002 Salt Lake Games. He scored a goal in the tournament as Russia won the bronze medal. Russia invited him to play at the 2004 World Cup of Hockey, but as he was without an NHL contract at the time, Bure declined to play due to a lack of proper insurance in the event of injury.

Bure married actress Candace Cameron on June 22, 1996. They were introduced by Cameron’s Full House castmate Dave Coulier at a charity hockey game. The couple has three children: daughter Natasha (b. 1998) and sons Lev (b. 2000) and Maksim (b. 2002). Bure became an American citizen in December 2001. Bure cited his family as the reason he retired from hockey in 2005. He felt he could return from his surgeries, but wanted to spend time with his children and allow his wife to return to acting. Bure and his family are Christians.

Though his offensive production declined in 2000–01, Bure’s 27 goals was second on the team to Jarome Iginla’s 31 and he finished third with 55 points. He became embroiled in a power struggle with his coaches, first Don Hay who was dismissed mid-season, and then Greg Gilbert, as both wanted him play a more defensive-minded game. Bure struggled to adapt and at one point was held out of the Flames lineup by Gilbert in response. Bure was rumoured to have asked for a trade out of Calgary, and the Florida Panthers (who had acquired Pavel), Buffalo Sabres and New York Rangers were among the teams who showed interest in his services. On June 24, 2001, the Flames traded Bure, along with Jason Wiemer to the Panthers for Rob Niedermayer and a second round draft pick.

Bure remained with the Panthers as the 2002–03 season began, but his year was marked by an offensive slump. He was also hampered by a hairline fracture to his wrist after Keith Primeau slashed him during an early December game against the Philadelphia Flyers. With only 5 goals and 26 points in 46 games for Florida, Bure was traded on March 11, 2003, to the St. Louis Blues in exchange for defenceman Mike Van Ryn. Another knee injury, this time a sprained ligament, kept Bure out of the Blues lineup for much of the remainder of the season. He recorded two assists each in five regular season and six post-season games for St. Louis. After the season, the Blues placed Bure on waivers, and he returned to Florida upon being claimed by the Panthers.

Free of injury for the first time in two seasons, Bure was one of the Panthers’ offensive leaders in 2003–04. He reached 20 goals for the fifth time in his NHL career, and as the season’s trade deadline approached, was Florida’s leading scorer with 45 points. However, as the Panthers were out of playoff contention, they traded Bure to the Dallas Stars on March 9, 2004, in exchange for Drew Bagnall and a draft pick. Bure was placed on the Stars’ top line with Mike Modano and Jere Lehtinen, and he recorded 7 points in 13 games to conclude the regular season. Bure added three assists in five playoff games.

In 2007, Bure and his wife opened a Florida restaurant called The Milk and Honey Café, but closed the business when the family moved to California. They operate a Napa Valley, California, winery, Bure Family Wines. Bure developed an interest in wine early in his NHL career that he described as growing into a passion: “I fell in love with the behind-the-scenes work and being able to start from the vineyard and put it into a bottle. It’s an amazing process.” Bure modified the Russian imperial seal his great-grandfather stamped on his watches to use as his company’s label.

Bure returned to the ice in 2010 as a contestant on the second season of the Canadian Broadcasting Corporation’s figure skating reality show Battle of the Blades. The series was a competition that paired a former professional hockey player with a figure skater. Bure’s partner was Ekaterina Gordeeva. The pair won the competition and shared a $100,000 prize donated to charities of their choice. Bure’s donation was made to Compassion Canada.