The Revs will receive $75,000, plus an additional $75,000 if Bunbury meets certain performance-based metrics.
“I want to thank Teal for his eight years of dedicated service to the New England Revolution,” Revolution sporting director and head coach Bruce Arena said in a news release.
“Teal always gave his all for the club on the field and he brought that same passion to his tireless work in the community. We wish Teal all the best in Nashville.”
Bunbury, 31, leaves as the fourth-leading scorer in Revolution history with 45 regular-season goals and 21 assists over 231 appearances for the club since 2014. He added 12 playoff appearances and two postseason goals with New England.
This season, the Ontario native posted three goals in 29 appearances (12 starts) and helped New England to the Supporters’ Shield title and an MLS-record 73 points.
Bunbury played four seasons (2010-13) with Sporting Kansas City before joining the Revs, registering 19 goals and seven assists.
Elsewhere on Sunday, Sporting KC traded defender Jaylin Lindsey to hometown club Charlotte FC in exchange for up to $325,000 in general allocation money and LAFC acquired defender Franco Escobar from Atlanta United.
Nashville traded their 2022 first-round pick to the LA Galaxy for forward Ethan Zubak and the Houston Dynamo traded a 2022 third-round pick to the Galaxy in exchange for veteran defender Daniel Steres.