The sources said this was not the first time Bush had disclosed his intention to vote for Clinton.
The comments came during a receiving line for board members of the bipartisan Points of Light Foundation when Bush was speaking to Kathleen Hartington Kennedy Townsend, Robert F. Kennedy's daughter and the former Maryland lieutenant governor. There were roughly 40 people in the room, and it's not clear how many people heard him, though multiple sources did.
The Republican former president's embrace of the Democratic nominee represents a dramatic new chapter in the complicated three-decade-old relationship between the two most prominent families in American politics.
It's a stunning political move -- one that comes just 49 days from the election, and less than a week before Clinton and Donald Trump square off in their first debate.
Trump's campaign manager, Kellyanne Conway, told CNN's Erin Burnett Tuesday that she respects "the 92-year-old former president very much and his decision."
"It is ironic that he would vote for the wife of the man who knocked him out of the race," she added on "Erin Burnett OutFront." "But look, this was a bruising primary ... so I know there are a lot of hurt feelings there."
News of his support for Clinton came first on Facebook, when Kennedy Townsend posted a photo of herself with George H.W. Bush, along with the caption: "The President told me he's voting for Hillary!!"
Kennedy Townsend sits on the advisory board of the Points of Light Foundation.
Bush family representatives declined to respond publicly.
"The vote President Bush will cast as a private citizen in some 50 days will be just that: a private vote cast in some 50 days. He is not commenting on the presidential race in the interim," Bush spokesman Jim McGrath said in a statement.
But sources with knowledge of the conversation told CNN they were surprised and disappointed that Kennedy Townsend had publicly shared a private conversation with the former president.
Kennedy Townsend declined to comment through a spokesman at the Rock Creek Group, where she works as managing director. She later took down the Facebook post.
GOP's Trump divide
Trump's controversial candidacy has split the group of former Republican nominees. Mitt Romney has hammered Trump in speeches and on Twitter, calling him unfit for office. But former Kansas Sen. Bob Dole has endorsed Trump, as has Arizona Sen. John McCain -- though somewhat reluctantly, often referring to "the Republican nominee" rather than Trump by name.
Neither George H.W. Bush nor George W. Bush had weighed in on the general election -- even as Trump savaged George W. Bush's decision to go to war in Iraq. However, many of the 41st and 43rd presidents' Cabinet secretaries and national security officials have backed Clinton.
George H.W. Bush national security adviser Brent Scowcroft endorsed Clinton
in June, saying she "has the wisdom and experience to lead our country at this critical time." George W. Bush Commerce Secretary Carlos Gutierrez said on CNN
in August that he "would have preferred Jeb Bush, but I think Hillary is a great choice. I am afraid of what Donald Trump would do to this country."
And Louis Wade Sullivan, the Health and Human Services secretary under George H.W. Bush and the only African-American in his Cabinet, said this month
that "though my enthusiasm for Hillary Clinton is somewhat tempered, I certainly believe she is an infinitely better choice for president than Donald Trump."
But George H.W. Bush isn't speaking for his entire family. Marvin Bush, the former president's youngest son, has said he would vote for Libertarian Gary Johnson. George P. Bush, George H.W. Bush's grandson, has backed Trump.
And Jeb Bush, Trump's former primary rival, has said he won't vote for Trump or Clinton.
A representative for George W. Bush wouldn't comment on Kennedy Townsend's Facebook post or how George H.W. Bush would vote. The representative simply said George W. Bush is "spending his time working to keep the Senate in Republican hands and is not commenting on the presidential campaign."
The Bush-Clinton relationship
The evolving relationship between the Bush and Clinton families began in 1992, when Bill Clinton ran against -- and defeated -- incumbent President George H.W. Bush. Eight years later, with Clinton term-limited out of office, Bush's son, then-Texas Gov. George W. Bush, succeeded Clinton on a pledge to "restore honor and dignity" to the White House -- a not-so-subtle knock on Clinton's marital infidelity.
But Bill Clinton and George H.W. Bush have also spent their post-presidencies teaming up for philanthropic endeavors. And in recent years, Bill Clinton and George W. Bush have increasingly appeared together.
The two grew so close that George W. Bush has referred to Clinton as his "brother from another mother," and Clinton has said the two bonded over becoming grandfathers.
A Bush-Clinton matchup
Early in the 2016 campaign cycle, it appeared the two families could be headed for another showdown with the presidency on the line: Hillary Clinton was seeking the Democratic nomination, while former Florida Gov. Jeb Bush -- the 41st president's son and the 43rd president's brother -- was a Republican candidate and a fundraising powerhouse.
Even if George H.W. Bush hadn't endorsed Hillary Clinton, it was hard to envision him backing Trump.
Neither of the former Bush presidents attended the Republican National Convention in Cleveland, where Trump became the GOP's nominee -- with the Bush family staying out of presidential politics after Jeb Bush, denounced repeatedly by Trump as "low-energy," exited the race.
CLARIFICATION: This story has been updated to clarify the context in which George H.W. Bush made his comment about voting for Hillary Clinton.