Mozart in the Jungle, meanwhile, was renewed for a fourth season. Both seasons will premiere later this year on Amazon's Prime Video subscription streaming service.
"Amazon Studios has been built by the risky, creative genius of shows like Mozart in the Jungle and Red Oaks," Amazon Studios head of comedy and drama Joe Lewis said. "We are excited to see how the amazing creators, casts and crews top themselves next season."
Mozart in the Jungle executive producer Roman Coppola added, "We're all delighted to be back for a fourth season and to share the further tales of our orchestra and all the artists who comprise it. For the fans who have been so enthusiastic about our show, we're so happy to have an audience that wants to see stories about the arts, music, and all these characters we've invented."
As for Red Oaks, creators Joe Gangemi and Greg Jacobs indicated they were happy they were able to wrap up their characters' storylines.
"We've always hoped to send these characters off to their futures with a third and final season, so we're thrilled that Amazon has given us the opportunity to do so," Gangemi and Jacobs said.
Mozart in the Jungle won the Golden Globe for best musical or comedy series in 2016, with star Gael Garcia Bernal also taking home an award for his performance, and both the series and Bernal were nominated for Golden Globes in 2017.