Rumours first surfaced late on Tuesday that he might take the decision with a number of general council members expressing to Eyewitness News that he was under increasing pressure.
Vice president Mark Alexander will serve as the acting president until an election can be held, SA Rugby confirmed.
Hoskins served as president from 2006 and was under pressure from a number of provincial unions wanting to see him replaced. The unions are currently meeting in Johannesburg to discuss a variety of issues in South African rugby.
Earlier this year, Hoskins attempted to have CEO Jurie Roux stood down over a draft report that implicated Roux in the misappropriation of funds, while employed previously at stellenbosch university.
