Bill Clinton, George W. Bush yuk it up

• Bush and Clinton's genial relationship now that both have left office is on full display


• The duo is in Washington on Monday to announce a new leadership program


• Bush calls Clinton an "awesome communicator," finds "a lot to admire"


• Clinton says he "learned a lot watching (Bush) over the years"

Washington (CNN) -- Bill Clinton and George W. Bush sounded like old college buddies when they appeared in Washington on Monday.

You'd never know that Clinton was the candidate who made Bush's father a one-termer, or that Bush ran for office in 2000 promising to restore "honor and dignity to the White House" after Clinton left.

Things are genial now that both men have their presidencies behind them and are focused on their legacies as former presidents. They appeared together on Monday to announce a new leadership program through their respective foundations.

But at times, it appeared the announcement took a back seat to the presidents' relationship. The two former commanders in chief joked with and about each other, told stories about their relationship, and even offered commentary about the number of selfies each is asked to take.

"He used to call me twice a year, in his second term, just to talk," Clinton said about Bush. "We'd talk -- depending on how much time he had, 'cause he was busier than me -- somewhere between 30 and 45 minutes, for several years. It meant a lot to me."

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Clinton said he and Bush "talked about everything in the right world. He asked my opinion, half the time he disagreed with it. But I felt good about that, I thought that was a really healthy thing."

Bush and Clinton were together Monday to announce the Presidential Leadership Scholars program, a partnership between their respective presidential centers, as well as George H.W. Bush's and Lyndon B. Johnson's centers.

The program's aim is to bring "motivated leaders across all sectors an opportunity to study presidential leadership and decision making and learn from key administration officials, practitioners, and leading academics."

It is well-documented that Clinton has grown closer with the Bush family since his presidency. Clinton and George H.W. Bush worked together after the Asian tsunami in 2004 and Hurricane Katrina in 2005, while Clinton and George W. Bush worked together after the 2010 Haitian earthquake.

Monday's event was a mutual admiration festival. As Clinton heralded their post-presidency friendship, he regularly touched Bush's arm. When the Arkansas Democrat reflected positively on Bush's father, George H.W. Bush, Bush 43 looked at Clinton and said, "Thank you, you are right."

When Bush gave Clinton advice on becoming a grandparent -- "Get ready also to be, like, the lowest person in the pecking order in your family" -- the two laughed and shared a hearty handshake.

Bill and Hillary Clinton are expecting their first grandchild this fall as their only daughter, Chelsea Clinton, is pregnant. Hillary Clinton attended Monday's event and sat near the back.

During the event, Bill Clinton's phone rang and the former president joked that "only two people have this number and they are related to me."

"I hope I'm not being told I'm about to become a premature grandfather," Clinton said to a chorus of laughs.

The former presidents were asked to reflect on each other's leadership qualities.

Clinton said Bush was decisive and did what he thought was best for the country, even if Clinton sometimes disagreed with him.

"I actually learned a lot watching him over the years," Clinton said.

Bush, in a briefer answer, said Clinton was an "awesome communicator" who can "really lay out a case and get people all across the political spectrum to listen."

"[There is] a lot to admire about Bill Clinton," Bush said, before noticing that he had said less than Clinton had.

"Is that enough?" Bush said. "It was a lot shorter than your answer, I know."

The differences between Bush and Clinton were also on full display. Clinton offered wordy, detailed answers, while Bush used more folksy one-liners and quips to engage the crowd. Both joked about how Bush often said he "didn't do" nuance.

Clinton said that before the event they "were laughing about having to go to restaurants and having to spend our time taking selfies" with fans.

Without skipping a beat, Bush said, "At least they are still asking, you know."

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CNN's Kevin Bohn contributed to this report.