Boston traded Tyler Seguin, Rich Peverley, and Ryan Button; in exchange, they acquired Morrow, Loui Eriksson, Reilly Smith, and Matt Fraser.

Despite Montreal dwindling in the standings, Morrow contributed with his best season performance in recording 5 goals and 11 points in 38 games.

[7] Having gone unsigned over the summer, Morrow was invited to attend the New York Rangers training camp on a professional tryout basis on September 12, 2019.

On July 15, 2020, Morrow agreed to a mutual termination of the remaining year of his contract with Dinamo Minsk, releasing him as a free agent.

[15] As a free agent in the following off-season, Morrow signed a one-year contract to continue in the KHL with HC Sochi on July 7, 2022.

[16] After a spell in Switzerland with HC Davos, Morrow joined UK EIHL side Manchester Storm in September 2023.