David Beckham's eldest son -- who's just 22 years old, BTW -- and Nicola just snapped up a gorgeous estate in Beverly Hills ... for a whopping $10.5 million, no less. We're told that's a mil over what the asking price was for this place, so you can tell they really wanted it.

Makes sense to us -- the 5-bedroom, 5.5 bath two-story mansion is a modern-day beaut in every respect ... just check out these photos, and you'll see what we're talking about.

Aside from the vast number of windows surrounding the home -- which we're sure is great for natural lighting -- the crib comes with luxury perks such as a private yoga room/gym, a dry sauna, a steam room, a juice bar, and yes ... there's a sweet pool on site too.

Don't even get us started on the views ... the house is tucked away in a canyon area, and it's overlooking a good portion of L.A. It's an awesome purchase -- one we're sure will serve them (and possibly their future family) well in the years to come. Major congrats!!!

Carl Gambino and Alexander Santaniello of Compass had the listing. Alexa Kort of Rodeo repped the buyers.