The Mayor of London accepted Miss Middleton's offer on Twitter after she laid down the gauntlet in a magazine column.
Writing in The Spectator, she mused over whether the Middletons or the Johnsons were the most competitive.
Mr Johnson, who claims ping-pong was originally a Victoria English invention called "whiff whaff", was quick to respond.
"I feel very nervous clearly because she seems to be very good. Well, she claims to be very good," he said.
"But I'm very happy to do this because it's a chance to promote what we're doing with sports legacy London.
"We have greatly increased the number of people doing sports. If Pippa's kind offer can be used to promote that then I'm all for it."
Unfortunately, he then seemed to confuse Miss Middleton with her older sister Kate, the Duchess of Cambridge.
"Pippa Middleton. She's a duchess is she? Or isn't she just a sister of a duchess?," he asked.
Mr Johnson was speaking at Ealing Studios, home to the Downton Abbey set, after announcing a £750,000 investment in London's TV and film industry.
At the studios, he attempted directing an animation scene in the special effects studio which Andy Serkis, Gollum from The Lord Of The Rings, founded.
He joked: "Would I be interested in being in a film? You betcha. But no one's curiously made me an offer. I think the movie industry is moving along without me at the moment. Who would I have to play me? You mean, apart from Brad Pitt obviously."
It is not yet clear when or where the ping-pong showdown will take place.
Pippa, 29, hinted that she had some considerable skill in her column as she talked about pursuing "less demanding hobbies".
"I'm informed that Boris Johnson ... wants to be 'whiff-whaff' world king even more than he wants to be Prime Minister," she wrote.
"I'm also told the Johnsons are almost as competitive as the Middletons. So I'd like to lay down a challenge to the Mayor.
"My only stipulation is that I can use my favourite Dunlop Blackstorm Nemesis bat, which I used when I played in the Milton Keynes U13 National Championships, don't you know. Bring it on, Boris."