Describing more of the impetus behind this movement, Trump said that "people want to see borders, they don't necessarily want people pouring into their country that they don't know who they are and where they come from."
Although many arguments were made in favor of leaving the EU, one of the most popular explanations was that the bloc's open borders risked damaging the U.K.'s national identity and economic well-being.
Trump also said that Britons "took back control of their country. It's a great thing."
"People are angry, all over the world, they're angry," he said. "They're angry over borders, they're angry over people coming into the country and taking over. Nobody even knows who they are. They're angry about many, many things."
Asked if he meant in the U.S. or the U.K., Trump said: "There's plenty of other places. This will not be the last."
Scotland, which Trump was visiting Friday, overwhelmingly voted to remain in the EU.
He also released a statement following the vote:
The people of the United Kingdom have exercised the sacred right of all free peoples. They have declared their independence from the European Union and have voted to reassert control over their own politics, borders and economy. A Trump administration pledges to strengthen our ties with a free and independent Britain, deepening our bonds in commerce, culture and mutual defense. The whole world is more peaceful and stable when our two countries — and our two peoples — are united together, as they will be under a Trump administration.
Come November, the American people will have the chance to re-declare their independence. Americans will have a chance to vote for trade, immigration and foreign policies that put our citizens first. They will have the chance to reject today's rule by the global elite, and to embrace real change that delivers a government of, by and for the people. I hope America is watching, it will soon be time to believe in America again.
Clinton released the following statement:
We respect the choice the people of the United Kingdom have made. Our first task has to be to make sure that the economic uncertainty created by these events does not hurt working families here in America. We also have to make clear America's steadfast commitment to the special relationship with Britain and the transatlantic alliance with Europe. This time of uncertainty only underscores the need for calm, steady, experienced leadership in the White House to protect Americans' pocketbooks and livelihoods, to support our friends and allies, to stand up to our adversaries, and to defend our interests. It also underscores the need for us to pull together to solve our challenges as a country, not tear each other down.
—Reuters contributed to this report.