"Alex had a solid season last year with Minnesota," Cubs general manager Jed Hoyer said. "Given Fuji's injury, we felt it was the right thing to do and the right time."
Cubs manager Dale Sveum remembered Burnett after facing him when he was with the Twins.
"He has a pretty good arm, 93, 95 [mph], good run on his fastball," Sveum said. "He has the ability to throw a strike, breaking ball at any time. Not a lot of secondary stuff, but pretty decent velocity with pretty good movement on his fastball."
The Cubs' bullpen has already lost Shawn Camp, on the disabled list with a sprained right big toe, and now Fujikawa.
"Things were obviously lining up and going good," Sveum said. "We'll make do somehow."
Burnett made a career-high 67 relief appearances for the Twins last season, going 4-4 with 10 holds and a 3.52 ERA. He led the club in relief innings, and his 2.49 ERA prior to the All-Star break ranked fourth among American League relievers.
This season, Burnett was 1-0 with a 1.50 ERA in nine Minor League relief appearances between Triple-A Buffalo and Triple-A Norfolk. He made two relief appearances for Baltimore this month before he was designated for assignment on May 23.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.