Doubront said his leg has bothered him for a couple weeks and it's been slow to heal. The plan now is to get him healthy, and then decide the next step, Cubs manager Rick Renteria said.
The lefty, who made it clear with the Red Sox that he wanted to start, said he wasn't surprised to be traded, but never asked to be dealt.
"For the moment, I was surprised a little bit," Doubront said. "I said, 'It's a new beginning and a new journey here.' I'm happy to be here and be part of this team and be a starter is most important for me.
"I never said, 'Trade me,'" Doubront said. "I just want to start."
In 10 starts with the Red Sox this year, Doubront was 2-4 with a 5.19 ERA, giving up 29 earned runs over 50 1/3 innings. As a reliever, he has served up 11 earned runs over nine innings in seven games, with six of those runs coming in his last outing Monday against the Blue Jays.
There were reports after the game against Toronto that Doubront was "disinterested." He said that's not true.
"It was a bad day, a bad day for me," Doubront said. "I didn't go there to give up six runs. Nobody wants to do that."
Coming to the Cubs will give Doubront a fresh start. Cubs president of baseball operations Theo Epstein knows the lefty from their days together in Boston.
"I talked to Theo, and I'm going to do my job here," Doubront said. "They expect me to go out and do my job, and that's what I want to do. It's not going to take too long to be competitive again.
"I'm going to start a new journey right here," he 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.