Turner was designated for assignment by the Marlins on Tuesday when Brian Flynn was recalled from Triple-A New Orleans.
In 20 appearances this year, including 12 as a starter, Turner is 4-7 with a 5.97 ERA. He has 54 strikeouts in 78 1/3 innings.
"Just 23 years old ... has a really good arm," said Cubs president Theo Epstein. "We feel like we got him at a low point of value. There is plenty of upside left with him so we're excited about that."
The Marlins will receive Class A pitchers Tyler Bremer and Jose Arias from the Cubs.