"You made it possible for us to have a very interesting debate about two guys who look at the world very, very differently," Sanders told Kimmel.
"Oh boy, do you guys look at it differently," Kimmel said, laughing.
Kimmel told Sanders his goal is to bring the two men together. "I don't build walls, I build bridges," he said, making an obvious nod to Trump's campaign promise to build a wall along the U.S.-Mexico border.
And Kimmel's vested interest? "I feel like I should be the moderator of this debate, right?"
On Wednesday's program, Trump said he would welcome a debate with the Vermont senator. "If I debated him we would have such high ratings,” Trump told Kimmel. "If he paid a sum to charity I would love to do that."
Shortly after the show aired, Sanders took to Twitter, writing, "Game on. I look forward to debating Donald Trump in California before the June 7 primary."
Sanders followed up Thursday afternoon with another tweet, writing, "I am delighted that @realDonaldTrump has agreed to debate. Let’s do it in the biggest stadium possible."
As for having both Sanders and Trump on the show, Kimmel told Sanders, "I’m interviewing all the candidates so I can decide which one of them will be my running mate. Usually, I know vice presidents do it the other way around, but I’m not 'usually' and this is how I do it. I will say, if there’s anyone who knows the importance of having a good, solid No. 2, it’s Bernie Sanders."
Kimmel introduced the Democratic presidential hopeful as the "most popular 74-year-old in the United States" and the "biggest name to come out of Burlington since the coat factory."