Asked on Twitter if he was planning to stand in the 8 June vote, which Theresa May called for on Tuesday morning but which must still clear a vote in the Commons, Mr Banks replied: “Yes.”
Mr Carswell, who defected from the Conservatives in 2014, announced he was standing down from Ukip late last month to become an independent MP.
Mr Banks welcomed the departure of the party’s only MP, describing it as “a rare piece of good news for Ukip”.
Mr Carswell tweeted after the announcement by the Prime Minister of her intention to hold an election: “If you voted Ukip in 2015, it’s job done.”
In March, Mr Banks said that his membership of the party had been suspended, and that he intended to build his own political movement from his Leave.EU campaign group.
Party chairman Paul Oakden said Mr Banks had not been suspended from the party, but that his membership had lapsed and it would be up to Paul Nuttall if the businessman would be allowed to renew it.
The spat signalled the deep fractures between the party and its millionaire donor, who has been consistently critical of its leadership.
Theresa May calls for general election
Ms May and Downing Street have repeatedly insisted there would be no snap general election before the scheduled vote in 2020.
But in a surprise statement, she said uncertainty over Brexit meant she had changed her mind.
“Our opponents believe because the Government’s majority is so small that our resolve will weaken and that they can force us to change. They are wrong,” Ms May said.
“They under-estimate our determination to get the job done and I am not prepared to let them endanger the security of millions of working people across the country, because what they are doing jeopardises the work we must do to prepare for Brexit at home and it weakens the Government’s negotiating position in Europe.”