The official accounts of Barack Obama, Joe Biden and Kanye West also requested donations in the cryptocurrency.
"Everyone is asking me to give back," a tweet from Mr Gates' account said. "You send $1,000, I send you back $2,000."
Twitter said it was a "co-ordinated" attack targeting its employees "with access to internal systems and tools".
See more: https://www.bbc.com/news/technology-53425822