Wearing a marijuana cryptocurrency t-shirt, dark sunglasses, and a "Make America Great Again" hat, Rodman told CNN he is "just happy to be a part of it because I think I deserve it".
President Trump said during the signing ceremony that they have "developed a special bond".
Kim's full delegation has not yet been confirmed, but other prominent North Korean officials seen in photos included foreign minister Ri Yong Ho and Kim Chang Son - the man who has been in Singapore in recent weeks negotiating logistical details for the summit.
Nearly as if they had rehearsed this moment, Mr Trump entered from the right and Mr Kim from the left.
The summit marked the first between a sitting USA president and a North Korean leader.
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During a post-lunch stroll through the gardens of the Singapore hotel where the summit was held, Trump said the summit had gone "better than anybody could have expected". It's aimed at settling a standoff over Pyongyang's nuclear arsenal.
Trump said he is willing to meet with Kim "many times" in the process.
While advisers say Trump has been reviewing briefing materials, the president insists his gut instincts will matter most when he gets in the room with Kim.
While the president has more recently sought to temper expectations of what he may be able to achieve with the summit, he has also said the interaction amounts to a crucial test in determining whether Kim is genuine in committing to rid his country of its nuclear program.
Mr Trump said he felt "really great" about the meeting.
As the two leaders met, Singapore navy vessels, and air force Apache helicopters patrolled, while fighter jets and an Gulfstream 550 early warning aircraft circled.
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For Mr Trump, he's likely to credit any success in these talks to his "maximum pressure campaign".
Trump made the comments as he and Kim walked together along balcony as they headed to a larger meeting with aides.
President Trump says a lot of "good will" and "hard work" went into historic document, says he has developed a "special bond" with North Korea's Kim Jong Un. His public statements and state-run media indicate he wants a deal to ease sanctions, but that he won't give up his nuclear weapons until he feels safe enough to retain power without them.
And until denuclearisation takes place, sanctions against North Korea would remain in place, he stressed.
Yet the top US diplomat added Trump is ready to offer "unique" guarantees to ease the regime's concerns about giving up a nuclear arsenal that provides a deterrent against foreign adversaries while also serving as a key point of national pride.
Trump finds time to tweet before meeting with Kim Jong Un
Pompeo said these guarantees would be "different and unique" than America has been willing to provide before. The North has faced diplomatic and economic sanctions over its nuclear and ballistic weapons programs.