One of George Bush’s lesser-known legacies was the role he played in cementing a modern presidential tradition: leaving a letter of support for the incoming commander in chief on Inauguration Day.

During the 2016 presidential election, an image of President Bush’s letter to the man who defeated him, Bill Clinton, was widely publicized, with many commenting that it was a refreshing reminder of the potential for bipartisanship during a bitterly divisive campaign. Mr. Bush, a Republican, left the letter for his Democratic successor on the Chesapeake and Ohio Railway desk in the Oval Office on Inauguration Day in 1993.

“Your success now is our country’s success,” he wrote. “I am rooting hard for you.”

Mr. Bush left his message of unity despite his contentious campaign against Mr. Clinton that denied him a second term.

Mark K. Updegrove, a presidential historian who wrote a book about the Bush family, said Mr. Bush, who died on Friday night at age 94, continued the custom after Ronald Reagan left him a lighthearted note during their White House transition in 1989.