As a youth, Megna played in the 2003 Quebec International Pee-Wee Hockey Tournament with the Chicago Young Americans minor ice hockey team. He played high school hockey at Glenbrook North High School and Tabor Academy. He graduated in 2009 and then went to the USHL where he played two seasons with the Cedar Rapids Roughriders. After two seasons with Cedar Rapids, Jayson went to University of Nebraska at Omaha where he played on the same team as his brother Jaycob Megna. While there, Jayson was named to the WCHA All-Rookie Team. Following his freshman year Jayson attended the Pittsburgh Penguins development camp and on August 1, 2012 he signed a two-way contract with an annual value of $925,000. In the 2013–14 season, on October 24, 2013, Jayson was recalled from the Wilkes-Barre/Scranton Penguins. He made his NHL debut versus the New York Islanders on October 25, 2013. He scored his first NHL point, an assist, and also his first NHL goal against the Carolina Hurricanes on October 28, 2013. On July 1, 2015, Megna left the Penguins organization as a free agent and signed a one-year, two-way contract with the New York Rangers. He began the 2015–16 season with the Rangers' AHL affiliate the Hartford Wolfpack, and was promoted to the Rangers on November 30, 2015. Megna returned to the Wolfpack on January 22, 2016 for a brief stint. He was later recalled by the Rangers on April 20, 2016, from the team's AHL affiliate, the Hartford Wolf Pack. With his contract with the Rangers completed, Megna secured a one-year, one-way deal as a free agent with the Vancouver Canucks on July 1, 2016. He was reassigned to the Canucks' AHL affiliate, the Utica Comets to start the season but was recalled to the Canucks on October 24, 2016. On December 8, 2016 he scored two goals to help the Canucks defeat the Tampa Bay Lightning by a score of 5–1 for his first career multi-goal game. On April 2, 2017, Megna signed a one-year extension with the Canucks for the season. On July 1, 2018, Megna signed as a free agent to a one-year, two-way contract with the Washington Capitals for the season. Playing with the Capitals AHL affiliate, the Hershey Bears, Megna was used in a top six forward role to produce 20 goals and 43 points in 71 games during the regular season and added 8 points in 9 postseason outings. As a free agent from the Capitals, Megna agreed to one-year, two-way $700,000 contract with his fifth NHL club, the Colorado Avalanche on July 1, 2019.
