Speaking to The Times, he said it was possible to go to a dinner party and assume no one was religious.
Dawkins, who has previously described himself as a "cultural Anglican", said the value of religion historically was merely "artistic".
"I think on the whole we [atheists] are winning," he told the newspaper. "We are all moving in the same direction. I get the feeling more and more that religion is being left behind."
The outspoken atheist launched his new memoir, An Appetite for Wonder, this week, at which he said he wanted to be remembered as "a believer in the possibility of discovering objective truth by scientific research".
He courted controversy earlier in the month when he claimed on Twitter that the last great achievements from Muslims happened in the Middle Ages.
He tweeted: "All the world's Muslims have fewer Nobel Prizes than Trinity College, Cambridge. They did great things in the Middle Ages, though."
He has made similarly provocative comments in the past, describing the Catholic Church as "evil" and describing the Pope as "a leering old villain in a frock".