The one-year deal is worth $1.5 million. Cleveland.com was first to report the agreement.
Felton averaged 9.5 points and 3.6 assists last season with the Mavericks. He's a career 41.2 percent shooter, 32.7 percent on three-pointers.
Felton, who has averaged 12.4 points and 6.0 assists over 11 seasons, will back up Chris Paul at point guard.
In other personnel news Thursday, the Clippers also signed Diamond Stone, their 40th overall pick in this year's draft.
Stone averaged 12.5 points, 5.4 rebounds and 1.6 blocks in his only season at Maryland; the 6-foot-11 center set the school freshman record with 39 points against Penn State on Dec. 30, 2015.
Stone averaged 10.4 points and 5.6 rebounds in five games with the Clippers' team in the Orlando Summer League.
Information from ESPN's Tim MacMahon and the Associated Press was used in this report.