Cooper and his former partner Benjamin Maisani split in 2018 after nearly a decade together but remained close friends and decided to co‑parent. Maisani was present at the birth of their first son, and in 2022 he formally adopted Wyatt, making the family unit official.
Wyatt arrived via surrogate and was announced by Cooper days later. He was named after Cooper's father, Wyatt Emory Cooper, who died when Cooper was 10; Wyatt's middle name, Morgan, comes from his mother’s family. At birth he weighed 7.2 pounds. Wyatt calls Anderson “Daddy” and Maisani “Papa,” and Cooper has shared tender anecdotes like missing Wyatt's first steps while on a work trip to Israel.