The leader will be announced at the party conference in Torquay, which, according to reports, Nigel Farage will not be attending.
Based in Folkestone, the former soldier and police officer was considered to be a front-runner in the contest and had seen the odds on him winning fall dramatically in recent weeks.
At the 2015 general election, Ukip won an extraordinary 13 per cent of the vote - beating the Liberal Democrats into fourth place - but was left with only one MP, Mr Carswell.
Although he did not name her, his comments appeared to be aimed at defeated leadership hopeful Anne Marie Waters, the controversial Sharia Watch founder who has denounced Islam as "evil".
The emergence of Ms Waters as a candidate in August prompted MEP Mike Hookem to resign his position as party whip in protest, with the MEP stating that he could not "turn a blind eye" to her "extreme views".
On Friday, Mr Bolton told members on the conference floor: "I do not see myself now as simply being your leader, I see myself as serving this party".
Bolton won 3,874 votes, ahead of 2,755 for Waters.
"The other thing is, I do not believe for a moment that we should be pushing this out and allowing the negotiations to be endless before we leave".
UKIP has a new leader..
Indeed, Mr Bolton had said that UKIP was in danger of becoming the "UK Nazi Party" if it plumped for Ms Waters (Ms Waters herself has vigorously denied this sort of claim).
The Ukip leadership election was called following the resignation of Paul Nuttall in the wake of the party's disastrous showing at the 2017 election. The most obvious way for the party to regain its mojo would be if Theresa May (or a new Conservative leader) sought to negotiate a close relationship with the European Union by, say, remaining in the single market. She resigned after just 18 days in the post, saying she could not work with the party hierarchy.