The 44-year-old Wells was designated for assignment by San Diego Aug. 10, and became a free agent after clearing waivers.
The Dodgers, in third place in the NL West, 5 ½ games back of first-place Arizona, hope Wells will be a catalyst for a strong stretch run, and a positive addition to their up-and-down starting rotation.
"David is an established veteran and has a long track record of success," said General Manager Ned Colletti on the Dodgers' Web site. "He's a true competitor who has pitched well down the stretch numerous times and we believe he can do so again this season."
Wells is 5-8 this season. He has 33 walks and 63 strikeouts, with an ERA of 5.54 in 118 2/3 innings and 22 starts.
Right-hander Brett Tomko was designated for assignment.