According to Eonline.com, Arquette proposed during a family dinner at Mastro's Ocean Club in Malibu, Calif. The actor and Cox's daughter Coco, 10, and his and McLarty's two-month-old son Charlie were present.
He said earlier this year of his son and McLarty: "It's all new, but it's all beautiful. Playing catch, making [his son] laugh, and seeing my girlfriend Christina being a mother for the first time and all the joy and love that it's going to bring her and me."
Last week, Cox revealed on Twitter that she was engaged to boyfriend Johnny McDaid of the band Snow Patrol.
Cox and Arquette split in 2010 after 11 years together.