The ex-soldier, who saw off a challenge from anti-Islam campaigner Anne Marie Waters, won with 30% of the vote.
He told the party conference: "Brexit is our core task however, it is not the end of the line."
Mr Bolton, who was backed by Nigel Farage, stood for UKIP as police and crime commissioner in Kent in 2016, coming second.
Who is new UKIP leader Henry Bolton?
Ms Waters came second in the leadership contest, with 21.3% of the 12,915 votes cast.
'Core purpose'
London Assembly member Peter Whittle, who had also been considered one of the favourites, came fifth.
Speaking at the UKIP conference in Torquay, Mr Bolton urged party members to "rally around the party", saying: "Without being united, we cannot lead."
Who is Henry Bolton?
A former officer and tank crew member, who served in Germany, Belize, Cyprus and Bosnia
Later became an officer with Thames Valley Police
Awarded on OBE in 2013 for services to international security and stabilisation
Has promised to "restore UKIP's credibility"
"We can't lead the nation and we can't hold the government to account and we can't achieve our core purpose at all," he said.
He promised to reorganise the party to increase its effectiveness and said he wanted to project UKIP "firmly and decisively into British politics for the good of the nation".
He praised the other six candidates and said he hoped they could continue to work together.
He said: "Today is not only a crucial day for our party, it is a critical day for our country."
Controversy about Ms Waters's candidacy had prompted threats from some MEPs that they would leave the party if she won. BBC political correspondent Ben Wright said Mr Bolton would be seen as the continuity candidate.
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. You are the party, not me. And this party needs to serve its country."
In 2005, Mr Bolton stood as a parliamentary candidate for the Lib Dems in Runnymede and Weybridge - the constituency held by the now chancellor Philip Hammond - coming third.
Paul Nuttall quit as UKIP leader after the general election, which saw UKIP's vote share shrink to 1.8% at the general election from 12.6% in 2015 - the year before the UK voted to leave the European Union.
His predecessor Diane James, who replaced Nigel Farage, lasted just 18 days in the job.
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