Kuggeleijn, the New Zealand international seamer, has been in the Indian Premier League bubble with Mumbai Indians as a reserve but moves to RCB following Richardson's decision to return home.
Richardson is one of several overseas players to curtail his involvement in this year's competition as the Covid-19 crisis worsens in India.
Adam Zampa and Andrew Tye have also decided to walk away from the tournament, while Ravichandran Ashwin is also stepping back to be with his family as the novel coronavirus infects Indians are a rate of more than 300,000 new cases per day.
IPL organisers have given permission to franchises to sign replacement players from other teams to fill empty spaces on their rosters in the event of player departures.
Kuggeleijn has previously represented Chennai Super Kings in the IPL.
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