Gibson was born and raised in Finland before he moved to Saskatchewan at age 15 to attend Notre Dame College. In his first season, he helped the midget AAA team win the Telus Cup national championship. He was selected by Chicoutimi of the Quebec Major Junior Hockey League as the No. 1 goaltender in the 2009 Canadian Hockey League import draft.

Gibson was selected in the second round (No. 49) by the Los Angeles Kings in the 2011 NHL Draft. But after playing two more seasons with Chicoutimi, he did not sign with the Kings and signed with the Toronto Maple Leafs on July 19, 2013.

Gibson split the 2013-14 season between Orlando of the ECHL and Toronto of the American Hockey League. He played all of 2014-15 in the AHL and went 24-17-3 with a 2.42 goals-against average and .921 save percentage for Toronto. He was traded to the New York Islanders on Sept. 17, 2015.

On Jan. 2, 2016, Gibson made his NHL debut with the Islanders, allowing one goal on 17 shots in relief of Thomas Greiss. He got his first NHL start on April 6, 2016, against the Washington Capitals and made 29 saves in a 4-3 overtime win that clinched a playoff berth for the Islanders.

Gibson won his first six games for Bridgeport to start the 2016-17 season, but he missed the rest of the season with a knee injury. He went 19-14-3 for Bridgeport in 2017-18 before being recalled by the Islanders. Gibson went 2-3-2, and one of his wins was a 50-save performance against the Calgary Flames on March 11; he became the first Islanders rookie since Billy Smith on Nov. 22, 1972 to make at least 50 saves in a game.

NOTES & TRANSACTIONS

• QMJHL First All-Star Team (2011)
• Signed as a free agent by Toronto, July 21, 2013.
• Traded to NY Islanders by Toronto with Carter Verhaeghe, Tom Nilsson, Taylor Beck and Matt Finn for Michael Grabner, September 17, 2015.
• Signed as a free agent by Tampa Bay, October 9, 2020.
• Signed as a free agent by Florida, July 28, 2021.