Putnam was 1-1 with four saves and a 3.26 ERA in 17 games with Iowa. He had 22 strikeouts over 19 1/3 innings. The right-hander, whom the Cubs claimed off waivers from the Rockies, was one of the last players cut in Spring Training. He appeared in 11 Cactus League games and gave up four runs on 14 hits over 10 innings while striking out six.
Putnam was a little surprised at the call, and caught an early morning flight from Nashville, Tenn., to get to Wrigley Field in time for Thursday's afternoon game against the White Sox.
"I feel I've been throwing well in Iowa," he said. "I didn't know they were ready to make a move this soon but, obviously, I'm thrilled.
"I had a pretty good spring and was obviously disappointed when I couldn't break camp with the team," he said. "You have to keep on keeping on and I felt I started the season pretty well in Triple-A, so I'm happy to be up here."
He and Blake Parker were sharing the closer's role at Iowa.
"I've always loved pitching in the back of the bullpen," said Putnam, who retired the lone batter he faced in the seventh inning of Thursday's 8-3 win.
Burnett was claimed off waivers from the Orioles on Monday and made his first appearance Wednesday, giving up one hit in one inning against the White Sox.
"These waiver claims, it's being able to get arms in the organization and going from there," Cubs manager Dale Sveum said.
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.