This year, the party lost all of the 145 local seats it was defending and won just 1.8 percent of the vote in the general election.
However, Bolton will be aware that Waters proved by coming second in the contest that she speaks for a significant strand of sentiment among members.
He promised to pressure the government into a hard Brexit.
The shrinking band of Ukip activists appear to have heeded the message and to have stepped back from recasting it as a nationalist party pushing messages reminiscent of the BNP.
Ukip's new leader will set out his vision for how the party aims to re-establish itself as an electoral force on Saturday after his shock victory in the race to succeed Paul Nuttall.
The 54-year-old former soldier and police officer was chosen after a ballot was held by UKIP members.
"Brexit is our core task", he said.
"We want to be a confident and optimistic nation and we want to be a nation that is proud to be called British".
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Mr Bolton did not join UKIP until 2014, but quickly made an impression by becoming its candidate in Kent in the 2016 Police and Crime Commissioner elections. There is an issue to be discussed. 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.
Farage told Channel 4's Michael Crick that he voted for Bolton, describing him as the "most competent" candidate in the running.
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.
Bolton's victory was a shock to nearly all in attendance at the announcement in Torquay.
Bolton, who was backed by Farage, won the leadership nod ahead of Anne Marie Waters, a vocal anti-Islam campaigner who wants an end to immigration to Britain from Muslim societies.
Reacting to the news, UKIP MEP David Coburn tweeted: "Congrats to Henry Bolton thank God the very bad @AMDWaters or ghastly @prwhittle didn't win".
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. She resigned after just 18 days in the post, saying she could not work with the party hierarchy.