His latest photo shows the casual-looking actress sitting on the floor in a hotel hallway with their take away meal.
Affectionately naming the blonde 19-year-old, he wrote: “Late night take out with the bae.”
Chloe also shared a cute shot of her own earlier in the day.
The captionless picture shows David and Victoria’s offspring delicately planting a kiss on her head as they sit in the back of a car.
In a recent interview Chloe, who is currently promoting Bad Neighbors 2, briefly opened up about the pair’s relationship and what it’s like to date someone who is also in the public eye.
She told InStyle magazine: "It creates a mass frenzy and they follow you in separate cars so you can’t just run around and share little silly and cute moments.”
Brooklyn and Chloe all but confirmed that they're boyfriend and girlfriend when they spent time together last week.
As well as making their Instagram debut together, the teens were also clocked snuggling up while being chauffeured around the capital - the same photo she later shared.
While last month it was reported that Chloe had already met Brooklyn's parents during a family meal.
A source told PEOPLE : "It was a really fun family late-night dinner vibe. They were inseparable all night. They had a massive PDA thing going on.
"Chloe was stroking Brooklyn's arm, and at one point Brooklyn had his head on Chloe's shoulder. They definitely seemed like a couple."
