The former Ukip MP said the “fundamental reason” for the party was to bring the UK out of the Brussels bloc and it was still time to “celebrate” achieving that goal.
Theresa May will trigger Article 50 and begin the Brexit process on March 29, beginning the two-year countdown until it is complete.
Mr Carswell will now become an independent member of Parliament for Clacton.
Speaking on the BBC, he said: “Job done. On Wednesday Theresa May announces that she’s triggering Article 50. Ukip, my party, we were set up 23 years ago to get us out of the European Union. Job done, we’ve won.
Douglas Carswell said the country could be "absolutely certain" that Brexit was in "good hands"
We can be absolutely certain that Brexit is in good hands
“Obviously when you get into politics and people are elected to do things there are all sorts of things you can convince yourself you’re there to do.
“But you know, I think the fundamental reason for Ukip, certainly the reason that I made that switch and the reasons why I think millions of people around the country made the switch to Ukip was over the Europe question.
“We can be sure now, we can be absolutely certain that Brexit is in good hands, we are going to leave and all of the things that Vote Leave campaigned for are going to come to pass.
“It’s wonderful, this is a moment for celebration.”
The many faces of Nigel Farage Tue, March 14, 2017
UKIP leader Nigel Farage is certainly animated!
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Nigel Farage arrives at BBC Broadcasting House in London
Writing on his website, Mr Carswell said he would now focus on constituency issues.
He said: "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 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."
Ukip leader Paul Nuttall has released a statement, which reads: "Douglas was genuinely committed to Brexit, but was never a comfortable Ukipper."
Mr Carswell repeatedly called for Mr Farage to step down as leader during his tenure, with the latter calling the MP "irrelevant".