Unselected in the NHL Entry Draft, he was signed by the Canucks as a free agent after his freshman year with the Rochester Institute of Technology Tigers.

In his only college season, he was named Atlantic Hockey's Rookie of the Year, in addition to receiving All-Tournament and Third All-Star Team honours, while helping the Tigers to a conference championship.

[6] He had received interest from at least three other teams, including the San Jose Sharks, Ottawa Senators and Columbus Blue Jackets, but ultimately chose Vancouver.

[5] He later recorded his first NHL point on January 24, a second assist on a Dan Hamhuis powerplay goal, the final Canucks tally in a 7–1 win against the Dallas Stars.

On March 31, 2011, Tanev had to be helped off the ice during a game against the Los Angeles Kings after opposing forward Kyle Clifford pushed him head-first into the end-boards.

[12] Averaging 13 minutes of ice time per game over 29 NHL contests with one assist, Tanev was commended by Canucks head coach Alain Vigneault for being "very dependable...making the high-percentage plays."

[15] As the Canucks moved on to the Stanley Cup Finals against the Boston Bruins, Ehrhoff and Rome returned to action, temporarily sending Tanev back to the sidelines.

After dressing for three of the team's first five games, he was reassigned to the Chicago Wolves, Vancouver's new AHL affiliate (the Moose were relocated to St. John's, Newfoundland, after the Winnipeg Jets returned to the NHL).

On October 9, 2020, Tanev left the Canucks as a free agent after 10 seasons and signed a four-year, $18 million contract with fellow Western Canadian club, the Calgary Flames.

[24] On July 1, 2024, Tanev signed a six-year, $27 million contract with the Toronto Maple Leafs after being traded by the Stars in exchange for Max Ellis and a seventh-round pick in the 2026 NHL entry draft.

[26] In the tournament semifinal versus the United States, Tanev prevented a scoring chance by the Americans late in the third period, which would have resulted in a game-tying goal.

[27] Tanev's biggest moment came in the tournament final against Finland, recording 21:38 of ice time, including a team-high 8:37 in the third period as Canada defended their one-goal lead.

According to many observers, including Ray Ferraro and teammates Brendan Gallagher and Connor McDavid, Tanev was perhaps the best defenceman in the tournament in terms of his defensive play - he and his defence partner, Morgan Rielly, were not on the ice for a single goal against at even-strength.

Following his performance in Game 5 of the 2011 Stanley Cup Finals, teammate Kevin Bieksa also highlighted his calm on-ice demeanour, quipping that "he could have played with a cigarette in his mouth.