The 27-year-old, who was training with Sundowns in Nelspruit recently, is believed to have signed a two-year deal with the Brazilians.
Affonso scored four goals in 13 appearances in all competitions for Lima last season, having joined them from Argentinian side CA Tucuman at the beginning of the season.
He becomes the second signing that Sundowns have made after the club snapped up right back Nyiko Mobbie from Free State Stars.
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