ESPN's Adam Schefter reported the conditional pick is a seventh-rounder.
Jones appeared in one game as a rookie in 2016, going 6-of-11 for 96 yards and an interception in Buffalo's 30-10 loss to the New York Jets in Week 17.
Jones commented on the trade:
Sending a seventh-round pick to the Bills for Jones makes sense for the Chargers. Philip Rivers will turn 36 in December, and Kellen Clemens turned 34 in June. Jones gives the team a younger option at quarterback, even if he's limited to backup duties.
NFL.com's Chris Wesseling noted Jones also has experience working with Chargers head coach Anthony Lynn:
The Bills, meanwhile, still have some options at quarterback to back up Tyrod Taylor. They signed T.J. Yates in April and selected Nathan Peterman in the fifth round of the 2017 draft.