Speaking immediately after the announcement, Bolton said pressuring Theresa May's government into a hard Brexit will be UKIP's "core task" under his stewardship.
In a recent YouTube campaign film, he complained that "we have gone down the road of mediocracy and compromise, we don't like the idea of excelling of anything because we worry that it implies that somebody is less good".
Senior political journalists had never heard of him before 4pmtoday.
He told Iain Dale the new leader had his "full support" and would be on hand to offer any advice.
Former Ukip leader Nigel described Mr Bolton as a "a guy of achievement and a man of substance".
Under his leadership, the party will continue to position itself as a bulwark against a "soft" Brexit and to cry betrayal at any move away from a complete severing of connections with the European Union.
Controversy about Ms Waters's candidacy had prompted threats from some MEPs that they would leave the party if she won.
Mr Bolton said he believes in "old-fashioned, classical liberalism", but feels it has "lost its way a bit".
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. Bolton reportedly said he was "fine" with the new design.
Nigel Farage has got a bit of a reputation for pulling amusing faces.
Commenting on the transgender debate, he said: "I think we are getting a bit far when we are encouraging children in some cases to question their own sexuality, I think that is certainly going too far".
He said: 'I do not see myself now as simply being your leader, I see myself as serving this party.
A source told express.co.uk: "If Anne Marie Waters win the party won't exist in its current form in two years".
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 past year.
His predecessor Diane James, who replaced Nigel Farage, lasted just 18 days in the job.
After exactly three years as leader, Mr Farage resigned to fight the Buckingham seat of Commons Speaker John Bercow at the 2010 election, subsequently coming third with 17 per cent of the vote.
US Orders Diplomat Retreat from Cuba
Cuban Foreign Minister Bruno Rodríguez met with Tillerson on Tuesday and reassured the country was not involved in the attacks . As a result of the estimated 60% drawdown, the Havana embassy will provide only emergency services to US citizens.
- Texas says DHS wrong, hacker didn't target state
- 'Big decisions' needed on rebuilding Puerto Rico, Donald Trump says
- Piers Morgan defends Ben Stokes, he 'was fighting for gay guys'
- Area football teams, players take a knee during national anthem in protest
- San Juan Mayor: This Is A 'People Are Dying' Story
- Demi Lovato credits family intervention for her sobriety
- US Pulls Some Staff Out of Cuba After Bizarre Health Episodes
- Former President Obama, Bidens join Prince Harry at Invictus Games
- Is this the Mona Lisa, nude?
- Interview: US measures against Cuba negative, arbitrary, says analyst