The Tesla and Amazon CEO's and Microsoft co-founder, and celebrities including Kim Kardashian West and her husband Kanye West and former US President Barack Obama, are among those to have had their accounts compromised.
Some of the above accounts requested donations in the cryptocurrency.
A post on Gates' page read: "Everyone is asking me to give back. "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".
Jack Dorsey's firm stated: "We know they [the hackers] used this access to take control of many highly-visible (including verified) accounts and Tweet on their behalf."
Twitter insisted they are taking "significant steps" to limit access to their internal systems and the investigation is ongoing.
Twitter even stopped verified accounts from tweeting.
Dorsey tweeted: "Tough day for us at Twitter. We all feel terrible this happened."
Dr Alexi Drew from King's College London told the BBC it could have been far worse for Twitter.
He commented: "If you were to have this kind of incident take place in the middle of a crisis, where Twitter was being used to either communicate de-escalatory language or critical information to the public, and suddenly it's putting out the wrong messages from several verified status accounts - that could be seriously destabilizing,"