Tanev, a 23-year-old Toronto native, recorded seven points (two goals, five assists) and added 10 penalty minutes in 38 games with Vancouver last season.
The six-foot-two, 185-pound blue-liner has 10 points and 12 penalty minutes in 92 career games, all with Vancouver.
He originally signed with the Canucks as a free agent May 31, 2010.
Alberts, 32, appeared in 24 games last season, recording one assist, 32 penalty minutes and 39 hits.
The 6-5, 218-pound defenceman from Minneapolis has appeared in 449 career games, recording 55 points (eight goals, 47 assists) and 492 penalty minutes over eight NHL seasons with the Boston Bruins, Philadelphia Flyers, Carolina Hurricanes and Canucks.
Alberts was originally selected 179th overall in the 2001 NHL draft by Boston.