The pair shook hands for the media before heading to talks and dinner at the five-star Metropole hotel.
They are expected to discuss a roadmap for ridding the Korean peninsula of nuclear weapons in two days of talks.
There has been little progress on that and other issues since the first Trump-Kim summit in Singapore last year.
Mr Trump said he thought this latest meeting would be “very successful”.
Earlier, he tweeted in praise of the host country on Wednesday morning, writing: “Vietnam is thriving like few places on earth. North Korea would be the same, and very quickly, if it would denuclearize.”
“The potential is AWESOME,” he added.
What’s the Trump-Kim schedule looking like?
Their first encounter was scheduled to be a 20-minute one-on-one meeting. It will be followed by dinner with their aides, according to the White House.
The two leaders will attend a series of meetings together on Thursday, but their exact agenda is unknown.
All major events – contractors or major press conferences – should be held on Thursday
- North Korea’s sidelined human rights crisis
- Sexual abuse of women ‘common’ in N Korea
Kim Jong-un carried out a brutal purge after taking charge of the country in 2011, ordering the death of his own uncle to secure his position.
According to the Korea National Security Strategy Institute, from 2012 to 2016, about 140 senior officials and government officials were executed.
As the country allocates funds for military and nuclear programs, food, fuel, and other basic needs are expanded and tightly controlled by the government.
Why are the leaders meeting again?
The Hanoi meeting is expected to build on the groundwork of what was achieved at the Singapore summit last June.
The meeting led to an opaque consensus, and the two leaders agreed to an “attempt at denuclearization.”
Diplomacy has hardly progressed since the summit. This time, the leaders of the two countries recognize the need for criticism for signs of true progress.
Trump, however, seems to live up to expectations on the eve of the summit and said that he is “not in a hurry” to insist on North Korea’s denuclearisation
“I don’t want to rush anybody. I just don’t want testing. As long as there’s no testing, we’re happy,” he said.
Washington had previously said that North Korea had to unilaterally give up its nuclear weapons before there could be any sanctions relief.
This is an ideal place for various reasons. He is always hostile to the United States, but has diplomatic relations with the United States and North Korea. This can be used as an example of US collaboration and cancellation of previous claims.
- Why Kim will be looking closely at Vietnam
- What North Korea can learn from Vietnam’s women
Vietnam has been open to foreign investment in recent decades and has become one of the fastest growing economies in Asia, but Vietnam and North Korea are communist countries.