The 80-year-old businesswoman and TV personality first met Davidson, 28, in 2015 at the Comedy Central Roast of Justin Bieber.
Stewart shared a clip of Davidson teasing her ahead of the pop star’s roast, accompanied by the caption: “Seven years ago I was on the stage with a young upstart named Pete who was doing comedy on Saturday Night Live.
“Now that same Pete is all grown up, squiring gorgeous women around and appearing everywhere!”
Stewart also posted a photo of her posing with Davidson and his current girlfriend Kim Kardashian at the Washington event.
The occasion marked the couple’s red carpet debut since they began dating last October.
The pair have attended events together previously, but this is the first time they have appeared on the red carpet together and been officially photographed as a couple.
Kardashian also posted a set of photos of herself and Davidson at the event. The last photograph was of their hands intertwined.
She captioned the photo series: “White House din din.”
The couple’s relationship has been marred by a string of offensive comments made by the reality star’s ex-partner, Ye (the rapper formerly known as Kanye West). In one of West’s music videos for his song “Eazy”, he buries a cartoon version of Davidson alive.
Davidson addressed the feud with Ye in his first stand-up gig in three years last Friday (29 April).
The comedian opened his set, Entertainment Tonight reports, by joking that West’s claims that he has Aids must be correct because the rapper is a genius.