Bidding will start at $5,000 for the sweaters worn by character Dr. Heathcliff Huxtable on The Cosby Show during the 1980s and '90s.
"My mother and father were going through a storage closet, and I happened to be there and pounced on these sweaters," said Bill's daughter Evin.
"I told them that the price of what some of these sweaters might sell for could make a big difference in the lives of thousands of children."
The family established education charity Hello Friend in 1997 after Ennis William Cosby was murdered in Los Angeles.
The auction will be held on eBay's Giving Works section from June 2-12.