Bush had to use a pseudonym and the boy, seven when the sponsorship started, had no idea who he was.
Bush, under the name George Walker, helped to fund education and meals.
The boy, Timothy, learned his mentor's identity when he left the scheme at 17 and was stunned, the charity, Compassion International, said.
"Dear Timothy, I want to be your new pen pal," Bush said in his first letter in 2002, using the pseudonym, a combination of his first and third names.
"I am an old man, 77 years old, but I love kids; and though we have not met I love you already," he wrote.
"I live in Texas - I will write you from time to time - Good Luck."
'Have you heard of the White House?'
Compassion International is a Christian, humanitarian charity that helps children living in poverty.
The former president first learned about its child sponsorship scheme in 2001 during a Christmas concert in Washington.
It is thought his identity was kept secret because of concerns Timothy could be targeted if people learned he was corresponding with a former US president.
But this did not stop Bush from dropping hints in his letters, according to the charity's former president, Wess Stafford, who screened all the letters.
"He was known for being a trickster," Mr Stafford told the BBC.
"Timothy, have you ever heard of the White House?" Bush asked in one of his letters.
"That's where the president of the USA lives. I got to go to the White House at Christmas time. Here is a little booklet that I got at the White House in Washington."
Even Bush's family had no idea about the letters until years later, Mr Stafford said.
He met Bush's son George - also a former US president - at a state dinner in 2008 and told them about the sponsorship.
"Laura teared up," Mr Stafford said of George W Bush's wife, Laura Bush.
"George [W Bush] paused for a moment and said 'Yep, that sounds like my Daddy.'"
Along with letters, "Bush 41" also sent presents, including art supplies.
Bush received messages back from Timothy to thank him for his presents.
"Thank you for not forgetting me. You're so nice and good," read one letter.
When Timothy learned who his mentor was he said it was life-changing, although the charity has not been able to get in touch with him since.
"I love that one of the most powerful men in the world, without any fanfare, reached out to one of the poorest children in the world," said Mr Stafford.
"I have a feeling that he did a lot of good things that we don't know about and a lot of things we probably never will."
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