Jeb and other members of the Bush family were joined by four former presidents, ambassadors and sports stars at the service inside St Martin's Episcopal Church in Houston, Texas.
Addressing the congregation, the 65-year-old said: "The last time I was with her, I asked her about dying; was she ready to go, was she sad?
"Without missing a beat, she said, 'Jeb, I believe in Jesus and He is my saviour.
"I don't want to leave your dad but I know I'll be in beautiful place.'"
The wife of former President George H W Bush, Barbara Bush died at her home with family by her side on Tuesday at the age of 92.
St Martin's, the largest Episcopal Church in the United States, was filled during the funeral which was attended by Bill Clinton, Barack Obama and first lady Melania Trump.
The service came one day after more than 6,000 people attended a public viewing at the landmark to pay their respects to Bush, who was also known as "America's matriarch".
A burial ceremony later took place at the Bush Library, Texas University.
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