Turner, a former No. 2 overall pick of the Philadelphia 76ers, spent the past three seasons with the Blazers.
Bazemore had been with Atlanta for the past five seasons, making him the longest-tenured current Hawk before the trade. At 29 years old, Bazemore had been the third-oldest member of the Hawks behind Vince Carter (42) and Miles Plumlee (30).
The teams announced the deal early Monday night.
Bazemore started 35 of the 67 games in which he played last season, averaging 11.6 points, 3.9 rebounds and 2.3 assists while shooting 32.0 percent from 3-point range in his seventh NBA season.
Atlanta, I dont even know where to start. Want to thank the @atlhawks for the a tremendous run over the past five years. Lots of roots planted in this city! To the front office and management, thank you putting me in a situation to thrive! #RIPCITY LETS GET IT!! @trailblazers pic.twitter.com/JoR49ol0sd— Baze (@24Bazemore) June 24, 2019
Turner averaged 6.8 points, 4.5 rebounds and 3.9 assists while playing almost exclusively as a reserve. His 21.2 percent shooting from behind the arc was the worst of his nine-year, four-team career.
Both wing players are headed into the final year of their respective four-year deals.