Mr Carswell said he was leaving "amicably" and that there was no need to call a by-election in his Clacton constituency as he will not be rejoining the Tories or switching allegiance to another party.
His decision to sit as an independent follows a long-running feud with former leader Nigel Farage, who claimed the MP was "never Ukip" and had "sought to undermine us".
Ukip leader Paul Nuttall, who in February failed to get elected as an MP in what he called the "capital of Brexit" in Stoke-on-Trent Central, said Mr Carswell was due to face a grilling by party chiefs over whether he joined the party to restrict Mr Farage's involvement in the EU referendum.
Mr Nuttall said Ukip 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.
"This is not a surprise," the leader said.
"I was elected on a pledge to forge unity in the party, and have had many discussions with key players to try and make that happen, but it had become increasingly clear to me that some things were simply beyond reach.
"Douglas was genuinely committed to Brexit, but was never a comfortable Ukipper.
"On Monday, he had been due to meet with the National Executive Committee to answer various questions relating to longstanding issues, including published allegations that he had joined us in order to try to minimise Nigel Farage's involvement in the referendum.
"Our party has not benefited financially or organisationally from having Douglas in Westminster. With this in mind, his departure will make no difference to my ability or focus on delivering the reforms I promised when elected as leader.
"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."
Mr Carswell immediately faced calls to trigger a by-election from Ukip's biggest financial backer, Arron Banks, a close ally of Mr Farage.
Mr Banks wants to follow through on his threat to stand against Mr Carswell, but it is unclear whether he would be able to do it under Ukip's banner as he is no longer a member of the party.
The insurance tycoon, who funded the Leave.EU campaign in the referendum and gave £1 million to Ukip ahead of the 2015 General Election, said earlier this month that he would concentrate on a new political movement.
Andy Wigmore, a spokesman for Mr Banks, said: "The net has been closing in. There is a Ukip National Executive Committee meeting on Monday and he (Mr Carswell) knew he was for the chop, so jumped.
"He should call a by-election and Arron will stand against him."
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's spat with Mr Farage blew up earlier this month over claims that the MP played a role in blocking a knighthood for the former leader.
Leaked emails showed Mr Carswell joking that Mr Farage should be given an OBE "for services to headline writers".
The MP, who defected from the Conservatives in 2014, responded with a provocative late-night tweet saying "Knight night".
This prompted Mr Banks to declare he is ready to stand against Mr Carswell in the 2020 general election.
Mr Carswell was re-elected in Clacton at the 2015 General Election with a majority of 3,437, beating the Tories into second place.
But that victory was secured on a more slender majority than the 12,404 he achieved in the 2014 by-election, which was sparked by his defection to Ukip.