It's not yet known when Mujica will join the A's, who are in the middle of a three-game series in Seattle. Upon his arrival, the club will make a corresponding 25-man roster move.
Mujica, who turns 31 on Sunday, was designated for assignment Friday after posting a 4.61 ERA in 13 2/3 innings out of the bullpen for Boston. He allowed three home runs in that span, and opponents were hitting .294 against him.
The 10-year veteran has enjoyed past success, earning a trip to the All-Star Game in 2013 with the Cardinals, when he pitched to a 2.78 ERA in 64 2/3 innings. He owns a 3.79 ERA in 456 career appearances with five organizations.
"I've seen him from the other side," said A's manager Bob Melvin. "He's a guy that's pitched in any number of roles. From what I understand, he's a leader in the bullpen, a standup guy in the bullpen, and understands that whole dynamic, and that's probably a good thing for us at this point."
To clear a spot on the 40-man roster, the A's transferred right-hander Jarrod Parker to the 60-day disabled list.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.