Both sides were expected to complete the deal after Chicago claimed Turner off waivers on Wednesday.
Arias and Bremer have been assigned to Class A Greensboro. Both have had experience closing, while Arias has also done some starting.
The Marlins were in a precarious spot keeping Turner because the 23-year-old is out of Minor League options. He had struggled as a starter and in relief, posting a 4-7 record with a 5.97 ERA in 20 appearances, 12 of them starts.
"The Cubs were the club awarded with the claim," Marlins president of baseball operations Michael Hill said. "They had exclusive negotiating rights for his services. We just wanted to get as much quality as we could in the trade. We got two very good, young arms to help replenish the system."
Arias was 1-1 with a 1.77 ERA and three saves for Class A Kane County, striking out 51 batters in 25 relief appearances.
Bremer also began his season with Kane County, going 5-1 with 12 saves and a 2.43 ERA in 28 relief appearances, with 51 strikeouts. He was promoted to Advanced Class A Daytona in the Florida State League at the end of June and was 0-1 with a 4.70 ERA and 12 strikeouts in eight appearances.
Had Miami not finalized a deal with the Cubs, it could have pulled Turner back off revocable waivers and placed him on release waivers. In that scenario, Chicago would have run the risk of not being able to land Turner.
The team with the worst overall record would have had first choice. The Rangers and Rockies could have both been ahead of the Cubs.
Before the July 31 non-waiver Trade Deadline, the Marlins didn't shop Turner, because at the time, the club was seeking its own trade options. Miami ended up acquiring Jarred Cosart from the Astros, and the team attempted to land another starter, but a deal couldn't be completed.
"[Turner] was a name we had discussed," Hill said. "But it wasn't something we considered at the time, because we hadn't acquired Cosart yet. We were still allowing [Brad] Penny to pitch [in the Minors]. We didn't have the depth. We still wanted [Andrew] Heaney and [Justin] Nicolino to start in the Minor Leagues.
"Leading up to the Trade Deadline, if the right deal would have been there, it would have been something we would have considered. The right deal just never came up."