WASHINGTON — Around Labor Day in 1998, the historian Michael Beschloss took his friend, Jon Meacham, then a Newsweek writer, to Kennebunkport, Me., where Mr. Beschloss interviewed George Bush, the former president, at the family compound. After their conversation, Mr. Bush took both visitors on one of the hair-rising rides he loved to take on his speedboat.

That was the beginning of an unusually close relationship between Mr. Bush and Mr. Meacham, who went on to be a Pulitzer Prize-winning author, historian and, eventually, Mr. Bush’s biographer. In 2006, the former president granted Mr. Meacham access to his extensive diaries, both audio and written, and as their connection grew, the project evolved into “Destiny and Power: The American Odyssey of George Herbert Walker Bush,” a No. 1 New York Times best seller in 2015.

Another measure of that deeply personal connection — unusual for most historians and their subjects — will be on display Wednesday when Mr. Meacham delivers a eulogy for Mr. Bush at his funeral at Washington National Cathedral, one of four men the former president chose to perform that duty.

Initially, members of the Bush family were skeptical of Mr. Meacham, in part because of lingering ill will toward Newsweek magazine, which in 1987, before Mr. Meacham worked there, ran a cover story on Mr. Bush with the headline “Fighting the Wimp Factor.” It did not help that he was a frequent commentator on MSNBC. But he eventually won them over.