He beat Jeremy Hunt comfortably, winning 92,153 votes to his rival's 46,656.
The former London mayor takes over from Theresa May on Wednesday.
In his victory speech, Mr Johnson promised he would "deliver Brexit, unite the country and defeat Jeremy Corbyn".
Speaking at the Queen Elizabeth II centre in London, he said: "We are going to energise the country.
"We are going to get Brexit done on 31 October and take advantage of all the opportunities it will bring with a new spirit of can do.
"We are once again going to believe in ourselves, and like some slumbering giant we are going to rise and ping off the guy ropes of self doubt and negativity."
Mr Johnson thanked his predecessor, saying it had been "a privilege to serve in her cabinet". He was Mrs May's foreign secretary until resigning over Brexit.
The outgoing PM in turn congratulated her successor, promising him her "full support from the backbenches".
Foreign Secretary Mr Hunt said he was "very disappointed", but Mr Johnson would do "a great job". He said he had "total, unshakeable confidence in our country" and that was a valuable quality at such a challenging time.
Mr Hunt added: "It was always going to be uphill for us because I was someone who voted Remain and I think lots of party members felt that this was a moment when you just had to have someone who voted for Brexit in the referendum.
"In retrospect, that was a hurdle we were never able to overcome."
US President Donald Trump also sent his congratulations to Mr Johnson, tweeting: "He will be great!"
Almost 160,000 Conservative members were eligible to vote and turnout was 87.4%.
Mr Johnson's share of the vote - 66.4% - was slightly lower than that garnered by David Cameron in the 2005 Tory leadership election (67.6%).
The former London mayor and Uxbridge MP was the clear favourite throughout the contest, but a number of senior figures have already said they will not serve under him.
Education Minister Anne Milton tweeted her resignation just half an hour before the leadership result was due to be revealed.
She joins the likes of Chancellor Philip Hammond, Justice Secretary David Gauke and International Development Secretary Rory Stewart who have all said they disagree too strongly with Mr Johnson's Brexit strategy to work closely with him.
Boris Johnson will become our next prime minister.
A sentence that might thrill you. A sentence that might horrify you. A sentence that 12 months ago even his most die-hard fans would have found hard to believe.
But it's not a sentence, unusually maybe for politics, that won't bother you either way.
Because whatever you think of Boris Johnson, he is a politician that is hard to ignore.
With a personality, and perhaps an ego, of a scale that few of his colleagues can match. This is the man who even as a child wanted to be "world king".
Now, he is the Tory king, and the Brexiteers are the court.
The EU Commission's Brexit negotiator, Michel Barnier, said he was looking forward to working with Mr Johnson "to facilitate the ratification of the withdrawal agreement and achieve an orderly Brexit".
Mr Johnson has previously said the agreement Mrs May reached with the EU was "dead".
He has pledged the UK will leave the EU on 31 October "do or die", accepting that a no-deal Brexit will happen if a new agreement cannot be reached by then.
Guy Verhofstadt, the European Parliament's chief Brexit co-ordinator, said the parliament would hold an extraordinary meeting on Wednesday in response to Mr Johnson's election.
Jeremy Corbyn reacted to the news of Mr Johnson's victory by tweeting that he had "won the support of fewer than 100,000 unrepresentative Conservative Party members", but "hasn't won the support of our country".
"Johnson's no-deal Brexit would mean job cuts, higher prices in the shops, and risk our NHS being sold off to US corporations in a sweetheart deal with Donald Trump," the Labour leader continued.
"The people of our country should decide who becomes the prime minister in a general election," he added.
Newly-elected Lib Dem leader Jo Swinson said Mr Johnson had "shown time and time again that he isn't fit to be the prime minister of our country".
First Minister of Scotland Nicola Sturgeon congratulated Mr Johnson, but said she had "profound concerns" about him becoming prime minister.
The new leader also received congratulations from Arlene Foster, the leader of Northern Ireland's Democratic Unionist Party, whose support has kept the Conservatives in government since the 2017 general election.