Republican Bush had opposed gay marriage while in office, which led some to criticise DeGeneres, an openly gay liberal, for befriending him.
On Monday, during a taping of her television show, DeGeneres said: "I'm friends with George Bush.
"I'm friends with a lot of people who don't share the same beliefs I have."
Bush, who served two terms as US president, has also faced condemnation for leading the country into war with Iraq and Afghanistan.
DeGeneres interviewed Bush on her chat show in 2017.
DeGeneres said she and her wife Portia had been invited to watch the Dallas Cowboys play the Green Bay Packers at the stadium in Dallas on Sunday by Charlotte Jones.
"She's the daughter of Jerry Jones who owns the Dallas Cowboys. And we went because we wanted to keep up with the Joneses", said DeGeneres, with humour typical of her show.
She said Jones had "fancy" friends and then showed her fans a video she took from the game, panning quickly around until she rested on Bush sitting in the next seat. He looked perturbed by the closeness of the camera before breaking into a grin.