The deal is reportedly for $9.5 million, according to Heyman.
Drew, the younger brother of former Red Sox outfielder J.D. Drew, will give Boston a stopgap at short for the 2013 season and time to develop both of their young shortstop prospects Jose Iglesias and Xander Bogaerts.
The 29-year-old Drew hit .223 with 7 home runs in 79 games between the Diamondbacks and Athletics last season. He missed time at the beginning of the year recovering from an ankle injury that cut his 2011 season short. The last time he played a full season was in 2010 when he hit .278 and hit 15 home runs in 151 games for Arizona.
Drew, a lefty, has hit .265 with 77 home runs and 349 RBIs over his seven-year career.
The move follows Boston’s off-season plan, overpaying a bit to sign players to a short-term deal.