The Red Sox announced the trade Monday.
Elias was 1-0 with a 1.23 ERA in Triple-A Pawtucket this season. In 55 major league appearances, he is 15-21 with a 4.20 ERA.
The 29-year-old native of Cuba was originally signed by Seattle as a free agent in 2011. He was sent to Boston four years later in a trade with Carson Smith for Wade Miley and Jonathan Aro.
The Red Sox will receive a yet-undetermined player or cash.