Russell was 2-0 with three saves at Triple-A Iowa and had not allowed an earned run in seven games. Varvaro was 0-1 with a 4.09 ERA in nine games before getting designated for assignment by Boston, and the Cubs claimed him off waivers on Sunday.
Denorfia aggravated a hamstring injury on the bases in Monday's 10-9 loss to the Cardinals. He is batting .429 in 21 at-bats.
Chicago announced the moves Tuesday.