Biega was selected by the Buffalo Sabres in the 2006 NHL Entry Draft, but was not able to sign a professional contract until after he completed his NCAA play. Upon graduation, on May 27, 2010, Biega was signed by the Sabres to a two-year contract. On October 9, 2010 Biega made his professional debut playing in the American Hockey League with the Portland Pirates, and on November 20, 2010, scored his first professional goal to help his team to a 2–1 win over the visitingWorcester Sharks. He went on to play in 61 regular-season games with the Pirates during the 2010–11 AHL season and also played 12 playoff games during his rookie campaign. Biega began the 2011–12 season with the Rochester Americans, the new AHL affiliate of the Buffalo Sabres. On July 5, 2013, Biega agreed to a one-year contract as a free agent with the Vancouver Canucks. He was assigned to AHL affiliate, the Utica Comets for their inaugural season in 2013–14, appearing in a career-high 73 games for 22 points from the blueline. On July 1, 2014, Biega re-signed with the Canucks, on a one-year contract worth $600,000. He was called up to Vancouver after posting 10 points in 25 games with Utica. Biega made his NHL debut with the Canucks on February 16, 2015, scoring his first NHL goal in a 3–2 win over the Minnesota Wild. Biega started the 2015-16 season with the Comets where he was named captain at the start of the season. He was called up to the Canucks in mid-December and on December 20, 2015, Biega earned his first career assist. It came on a Jannik Hansen goal in a 5−4 shootout loss to the Florida Panthers. On February 2, 2016, Biega signed a one-way, two-year contract extension valued at $1.5 million. On February 28, 2018, Biega was again signed to a two-year, $1.65 million contract extension by the Canucks. On September 30, 2019, Biega was placed on waivers by the Canucks, prior to the start of the 2019–20 NHL season. He cleared waivers the next day. On October 6, 2019, Biega was traded by the Canucks to the Detroit Red Wings in exchange for David Pope. He made his debut for the Red Wings on October 15, in a game against his former team, the Vancouver Canucks. On March 9, 2020, Biega signed a one-year contract extension with the Red Wings.
Personal life
Biega's brother, Danny Biega, is also a professional ice hockey player who last played for the Carolina Hurricanes. He also has two other brothers, Marc and Michael. Alex, Danny, and Michael all played hockey for Harvard University becoming the first trio of brothers since 2000 to play for Harvard. Biega met his wife Diana while in Boston. They had a son together in April 2015.
