The 21-year-old had just four goals and six assists in 44 NHL games last season, and fell out of favor with the Jets. He was a restricted free agent this summer and the Jets retain his NHL rights.
Burmistrov is a native of Kazan, Russia. He played one game for Ak Bars in 2008-09 before leaving to join the Barrie Colts of the Ontario Hockey League.
When the Jets were still the Atlanta Thrashers, they made Burmistrov the No. 8 pick in the 2010 draft and inserted him into the lineup the next season. Burmistrov never had more than 28 points in an NHL season.