After a two-year junior career in the United States Hockey League (USHL), Alberts was selected by the Boston Bruins 179th overall in the 2001 NHL Entry Draft.

In his third college year, he recorded 16 points was a co-recipient of Hockey East's Best Defensive Defenseman award with Prestin Ryan of the Maine Black Bears.

In the playoffs, he ended what was the longest semifinal game in Hockey East history with a double-overtime goal against the Maine Black Bears.

[6][notes 2] Alberts earned Hockey East All-Tournament honors, as the Eagles defeated the New Hampshire Wildcats 3–1 in the final to win the Lamoriello Trophy as conference champions.

Making the Bruins' roster for the 2005–06 season, he made his NHL debut on October 5, 2005 in a game versus the Montreal Canadiens.

[4] Returning to the Boston lineup, he scored his first NHL goal late in the campaign during a game against the Buffalo Sabres on March 12, 2006.

[2] During his rookie season, Bruins head coach Mike Sullivan experimented with playing Alberts at the forward position for roughly a month.

Going down to his knees to block a puck moving into the defensive zone, opposing forward Scott Hartnell bodychecked him, using his elbow to hit Alberts' head against the boards.

[13] Alberts recovered in time to make his NHL playoff debut in April 2008, as the Bruins were eliminated in the first round by the Montreal Canadiens.

[14][15] After being a healthy scratch for the Bruins' first two games in the 2008–09 season, Alberts was traded to Philadelphia for Ned Lukacevic and a conditional 2009 draft pick on October 13, 2008.

[17] Alberts became an integral part of the Flyers' defensive corps, leading the team in hits (157) and ranking third in blocked shots (133).

[19] He continued to earn criticism from Vancouver fans and media in the playoffs, particularly for his lack of speed and for taking costly penalties.

[25] Shortly after recovering and returning to the lineup, he suffered another injury, breaking his wrist while blocking a shot during a game against the St. Louis Blues on February 14, 2011.

[26] He missed the remainder of the regular season,[4] finishing with a goal and seven assists, while leading Canucks defensemen with 113 hits, over 42 games.

During the off-season, Alberts was re-signed by the Canucks to a two-year, $2.45 million contract on June 29, 2011 (two days prior to his pending unrestricted free agency).