Former leader Nigel Farage recently called on Mr Carswell to quit, accusing him of "actively working against UKIP".
Party leader Paul Nuttall said Mr Carswell was "committed to Brexit, but was never a comfortable Ukipper". There are now calls within UKIP for the Clacton MP to call a by-election.
The party leader said Mr Carswell's announcement was "not a surprise".
He 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."
UKIP donor Arron Banks had previously indicated he could stand against Mr Carswell at the next election, amid a long-running feud over UKIP's future direction and strategy.
His spokesman, Andy Wigmore, said: "The net has been closing in - there is a UKIP National Executive Committee meeting on Monday and he knew he was for the chop, so jumped.
"He should call a by-election and Arron will stand against him."
On Twitter, Mr Banks posted a smiley face emoji and a green tick.
Mr Farage tweeted: "Carswell has jumped before he was pushed. He was never UKIP and sought to undermine us. He should have gone some time ago."
Political cartel
Mr Carswell chose to announce the decision on his blog, just days before the prime minister is due to formally notify the European Union the UK is leaving.
He said: "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."
He added: "I will not be switching parties, nor crossing the floor to the Conservatives, so do not need to call a by election, as I did when switching from the Conservatives to UKIP. I will simply be the Member of Parliament for Clacton, sitting as an independent.
"I will leave UKIP amicably, cheerfully and in the knowledge that we won."
Mr Carswell told the BBC News Channel he would will still be sitting in opposition "holding the government to account".
He declined to comment on where his decision left UKIP, saying there was a "political cartel" in the UK and he wanted to be part of "far-reaching change" as an independent MP.
Mr Carswell said: "I think the fundamental reason for UKIP - certainly the reason that I made that switch and I think the reason why millions of people around the country made the switch to UKIP, was over the Europe question."
The 2014 defection: "Only UKIP can shake up that cosy little clique called Westminster"
Earlier this month, Mr Carswell vowed to "absolutely" fight the next general election as a UKIP candidate.
He was speaking after Mr Nuttall urged senior figures to "stick together" after he unsuccessfully stood for Parliament at the Stoke Central by-election.
Mr Carswell, 45, first entered the Commons in 2005 as MP for Harwich, defeating Labour's candidate by just 920 votes. By 2010 he defeated the same opponent by 12,000 votes - although boundary changes had seen the seat renamed.
After defecting to UKIP he stood down to seek re-election in a by-election, which he won by 12,404 votes in October 2014. At the general election in 2015, he retained the seat with a 3,437 majority.
Another Tory MP, Mark Reckless, followed Mr Carswell's example by defecting to UKIP in 2014, but lost his seat the following year.
UKIP MEP Bill Etheridge said he was "delighted" as the "focus of serious infighting in the party has gone".
"But I think he needs to step down and call a by election... He was elected twice on a UKIP ticket, with UKIP resources and the hard work and shoe leather of UKIP activists."
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