Mr Trump said he would halt “war games” while Mr Kim had promised to destroy a missile testing site.
Their agreement also included a commitment from Mr Kim to rid the Korean peninsula of nuclear weapons.
It is the first time a sitting US president and North Korean leader have met.
The pair shook hands, held talks together and ate lunch accompanied by advisers.
It caps a remarkable turnaround for the two, who only last year were engaged in angry threats.
The summit centred on nuclear disarmament and reducing tensions.
The agreement said the two countries would co-operate towards “new relations” while the US would provide “security guarantees” to North Korea.
On nuclear weapons, Mr Kim “reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean peninsula”.
Announcing the agreement to reporters, Mr Trump said that Mr Kim had agreed to “verified” denuclearisation – a key US demand before the summit.
Mr Trump also said that he had raised the issue of human rights with Mr Kim, who runs a totalitarian regime with extreme censorship and forced-labour camps.
An Entrepreneur and Philanthropist. Editor-in-Chief of www.233times.com. A Senior Journalist with Ghanaian Chronicle Newspaper. An alumnus of Adisadel College where he read General Arts. He holds first degree in Bachelor of Arts from the University of Ghana; Political Science (major) and History (minor). He has also pursued MSc Corporate Social Responsibility (CSR) and Energy with Public Relations (PR) at the Robert Gordon University in the United Kingdom. He is a 2018 Mandela Washington Fellow who studied at Clark Atlanta University in USA on the Business and Entrepreneurship track. His mentors are Rupert Murdoch, Warren Buffet, Sam Jonah, Kwaku Sakyi Addo and Piers Morganview all posts by: Nana Kwesi Coomson
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