Terms were not announced but the former Boston Celtic was eligible for a four-year extension, local media reported.
Perkins was traded to Oklahoma City last week as part of a four-player deal.
"We had a unique opportunity to enter into discussions with Kendrick to solidify his future with our organization," Thunder General Manager Sam Presti said in a statement.
"Kendrick's blue-collar, team-first approach aligns with the vision we hold for building a sustainable team."
Perkins averaged 7.3 points and 8.1 rebounds in 12 games with Boston this season. He has yet to play for the Thunder because of a knee injury that is expected to sideline him for two to three weeks.
(Reporting by Gene Cherry in Salvo, North Carolina)