Alex Grant was born on January 20, 1989 in Antigonish, Nova Scotia. The Saint John Sea Dogs would draft him first overall in the 2005 QMJHL Entry Draft. As a product of the QMJHL, Grant was drafted by the Pittsburgh Penguins in the fourth round, 118th overall, in the 2007 NHL Entry Draft.
At the conclusion of his QMJHL career, Grant would make his professional debut with the Wheeling Nailers of the ECHL during the 2009-10 season. He would play portions of the next four seasons with Nailers and the AHL’s Wilkes-Barre Scranton Penguins before he was traded to the Anaheim Ducks for Harry Zolnierczyk.
It was with the Ducks organization where he would make his NHL debut on November 30, 2013 against the San Jose Sharks where Grant would score his first NHL goal. After being returned to the AHL’s Norfolk Admirals, Grant was traded to the Ottawa Senators for Andre Petersson.
On July 2, 2015, Grant would sign a one year contract with the Arizona Coyotes as an unrestricted free agent. He would spend the majority of the following season in the American Hockey League before signing with the Boston Bruins on July 4, 2016. He would go on to spend the entire 2016-17 season with the club's affiliate in Providence where he would lead all defenceman with 49 points.
As a free agent once again in the summer of 2017, Grant signed a deal with the Minnesota Wild.