Wells will now go through waivers. If he is claimed, the selecting team gets the right-hander and the remainder of his $2.7 million contract. If he gets through waivers he is expected to be assigned to the Triple-A Iowa roster.
Wells is 1-2 with a 5.34 ERA in 12 games, including four starts, this season.
Wells lasted three innings in a 5-3 victory over the New York Mets on Tuesday, giving up three earned runs on six hits, walking four and striking out three. Wells, who lost out on a spot in the starting rotation to Chris Volstad in spring training, took injured Ryan Dempster's spot and has struggled in his two starts.
Wells lasted 3 2/3 innings in a 7-0 loss to the Chicago White Sox on June 20, walking another four batters.
"The command and the walks still are a major issue that he's got to get better at," manager Dale Sveum said. "Those things are killing him and the pitch count gets up so high he can't even get to five innings. He's got to go down and get better at that."
Dolis has pitched in 23 games for the Cubs this season, including a stint as the closer when he saved four games. But he was plagued by control problems, walking 17 in 25 1/3 innings, and lost the job and eventually his spot on the 25-man roster.
Dolis had a 2.92 ERA with three saves in 11 games for Triple-A Iowa.
ESPNChicago.com's Doug Padilla contributed to this report.