The person confirmed the move to the AP on the condition of anonymity because the deal had not been announced. It was first reported by ESPN.
Griffin, 33, should help the defending Eastern Conference champions weather the absence of center Robert Williams III, who is expected to miss 8-12 weeks after knee surgery.
Seven-footer Luke Kornet sprained his ankle shortly after the start of training camp this week.
The 2009 No. 1 overall draft pick, Griffin is a six-time All-Star who averaged career lows of 6.4 points and 4.1 rebounds in 17 minutes with the Brooklyn Nets last season. In 12 NBA seasons, he averaged 19.8 points and 8.2 rebounds.
Blake Griffin is set to play for his fourth team since getting drafted first overall by the LA Clippers in 2009.