The ruling concludes a legal battle that began in 2013, when Marvin Gaye's family claimed Blurred Lines copied Gaye's 1977 hit Got to Give It Up.
Gaye's family initially won the case in 2015, but Thicke and Williams appealed.
A California court upheld the verdict in March this year, and the new amended judgement confirms the settlement.
Thicke, Williams and Williams' publishing company More Water From Nazareth are jointly required to pay Gaye's family damages of $2.8m (£2.2m).
