Both parties had up until 6 p.m. ET on Monday to agree on a rookie extension. Prince is set to make $3.4 million this season in the final year of his rookie deal.
Acquired by Brooklyn in an offseason deal with the Atlanta Hawks, Prince could be in line for some major minutes due to the extended absences of Kevin Durant (injury) and Wilson Chandler (suspension).
Prince averaged 13.5 points and 3.6 boards while shooting just under 40% from downtown last season. The 25-year-old forward was one of Brooklyn's best performers during the preseason, posting team highs in points (16.8) and 3-point percentage (69.6%).
The Utah Jazz drafted him 12th overall in 2016 and traded him to the Hawks in a three-team deal shortly thereafter.