Mr Carswell announced his decision to quit the party on Saturday, declaring "job done" as Theresa May prepares to trigger Brexit.
He admitted he had joined to try to ensure a less divisive Leave campaign in the EU referendum but senior party figures have suggested he was actively working against the party and that he quit before being kicked out.
The Clacton MP has denied that he was involved in "subterfuge".
He told Sky News: "The idea that I was involved in sort of subterfuge or some sort of covert operation is nonsense.
"I called a press conference in central London on August 28 2014 and I said at that press conference very clearly when I was announcing that I was joining Ukip, that Ukip and Euroscepticism needed to be positive and upbeat.
"When I won the Clacton by-election a few weeks later, I gave a speech where I said Euroscepticism to win the referendum needed to be a force that appealed to all Britain and all Britons, first and second generation as much as any other.
"I spent the referendum campaign arguing that the people running the campaign should be positive and broad-minded.
"I don't think any of this is something that I've kept secret, and it's no secret either that some in Ukip wanted to make sure that Ukip ran the referendum campaign.
"I've been pretty open about the fact that Eurosceptism to be a force for change needs to be inclusive, upbeat, progressive and forward-looking."
Mr Carswell also revealed he had not spoken to Mr Farage since around December and urged him to be more positive "about the fact that on Wednesday, we win" - referring to the Prime Minister's intention to invoke Article 50 to begin the UK's withdrawal from the EU.
Mr Carswell was due to face a grilling on Monday from party chiefs over the claims that he joined the party to restrict Mr Farage's involvement in the EU referendum.
And his departure follows a long-running feud with the former leader, who claimed the MP was "never Ukip" and had "sought to undermine us".
Ukip leader Paul Nuttall said the party has not benefited "financially or organisationally" from Mr Carswell's presence in the House of Commons and so his departure would make "no difference" to his reform agenda.
"Douglas was genuinely committed to Brexit, but was never a comfortable Ukipper,” he said.
"As we redefine our mission and take up the next phase of our campaign to rebuild a confident, independent nation, Douglas would have been increasingly out-of-kilter with our members' aspirations.
"We now have an opportunity to put behind us the most damaging internal conflict which has dogged us over the past year, and look forward with optimism and unity of purpose to the very real challenges of policing Brexit and further reforming the vigorous democracy of the UK."
Announcing his resignation on his blog, Mr Carswell paid tribute to party members and supporters, adding: "Like many of you, I switched to Ukip because I desperately wanted us to leave the EU.
"Now we can be certain that that is going to happen, I have decided that I will be leaving Ukip.
"I will leave Ukip amicably, cheerfully and in the knowledge that we won."
Mr Carswell was re-elected in Clacton at the 2015 General Election with a majority of 3,437, beating the Tories into second place.