The burly defender joins Amakhosi from SuperSport United, with whom he lifted the Nedbank Cup trophy at the weekend, with the player putting pen to a four-year deal in Soweto.
"We have been eyeing Morgan for almost two years and we are glad he has finally landed in Naturena. Morgan is one of the most reliable defenders in South Africa," Chiefs general manager Bobby Motaung told The Sowetan.
"The arrival of Morgan is further proof that we are serious about taking Chiefs back to glory days where we used to win trophies - it is starting next season.
"Morgan was contracted to SuperSport United, so we had to approach them. The same applies to Mulomowandau Mathoho; Bloemfontein Celtic informed us they are still looking for a replacement before releasing him.
"We have got the money but must respect others when they ask us to wait."
Gould is the second high-profile signing for the club in the off-season, with his national team-mate Siboniso Gaxa having joined two weeks ago.
Several players already on the books with the Glamour Boys have signed contract extensions, including striker Sthembiso Ngcobo (three years) and goalkeeper Arthur Bartman (one year).