Richardson, 22, can play at hooker or openside flanker.
Born in Pinetown, 16km west of Durban, he is understood to have Scottish ancestry.
He plays for the Sharks and is considered one of the rising stars of South African rugby. He featured in both matches when the Sharks played the British & Irish Lions in July.
Gregor Townsend has had his eye on Richardson for some time, according to the website IOL.
The Scotland coach had a spell in Super Rugby with the Sharks in 2004 where he was a team-mate of Eduard Coetzee, the former prop who is now chief executive of the Sharks.
It is understood that Townsend’s relationship with Coetzee helped open the door for Richardson to join the Scotland fold.
He is a former South Africa Under-20 international and was a member of their squad for the 2019 World Rugby Under 20 Championship.
Scotland play their first autumn Test against Tonga on October 30 at BT Murrayfield and then face Australia, South Africa and Japan over the following three weekends at the same venue.
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