Mass resignations, including 18 of the party's 20 MEPs, had been threatened if the far-right candidate, who has described Islam as evil, had won. Before joining UKIP, he stood as a parliamentary candidate for the Liberal Democrats.
The party is due to announce its new leader later at its conference in Torquay. She came second, with Bolton gaining over 1,000 more votes than her.
It is thought if Ms Waters wins the leadership contest it could create a huge divide in the party.
"When we leave the European Union, that is not the end of the story".
He said he was "absolutely delighted" that Mr Bolton had been elected, and added that it was "time to roll up our sleeves and get on with the task ahead".
Tensions high in Washington as a deadline looms for health care reform
In the absence of any independent assessment of what their proposal does, they made up numbers that ignore big chunks of the bill. There is only one reason the Senate is even considering a vote this week on the catastrophically flawed proposal from Sens.
Bolton distanced himself from the anti-Islam direction advocated by Waters and to a lesser extent by the early favourite, Peter Whittle, who finished a surprise fifth in the contest.
Quoting the "serve to lead" motto of the Sandhurst royal military academy - from which he was a graduate - Mr Bolton said: "I do not see myself now as being simply your leader, I see myself as serving this party".
Yet within the space of a year, the party has faced collapse with the departure of Farage. Bolton reportedly said he was "fine" with the new design.
There were a total of 12,915 votes cast in the leadership election, compared with the more than 300,000 secured by Jeremy Corbyn when he was re-elected as Labour leader previous year.
The party has been riven by splits and disagreements, one of which resulted in MEP Steven Woolfe being taken to hospital after a fight with another Ukip MEP.
"I didn't intervene directly in the election campaign but I did make it pretty clear without saying so that if we lurched towards the BNP-type position that I wouldn't stay part of it and nor would anybody else". Instead he suffered a hefty defeat in February's Stoke-on-Trent Central by-election and later resigned after leading the party to a disastrous result in the snap general election.