The Red Sox acquired Miller and outfielder Carlos Gutierrez from the Giants on Monday in exchange for infielder Marcelo Mayer (forearm), Jeff Passan of ESPN.com reports.
Miller will make his way to Boston in the midst of one of the more dominant stretches of his career. Dating back to June 12, the 28-year-old has delivered 14 consecutive scoreless appearances. The left-hander appeared to have worked his way into the Giants' unsettled closer picture, but with the move to Boston, he'll operate as a setup man in front of Aroldis Chapman.