The Amazon founder/multibillionaire hit the town Saturday in Milan -- where he and his fiancée, Lauren Sanchez, are visiting as he celebrates the big 6-0 in style. Emphasis on that last part ... 'cause, as you can see here, they left their hotel dressed to the nines.

JB was in an all-black getup ... rocking a leather jacket and some nifty shades, while his lady was in a matching black-and-white ensemble. Indeed, they look very power couple-y.

Of course, there were a ton of paps around snapping their exit, and Jeff made sure Lauren got into their waiting car first -- ever the gentleman. Gotta say ... dude's a bit of a butterfly.

By that ... we mean he's glowed up quite a bit over the past 2 decades -- especially ever since he got with Lauren. Jeff's in the best shape of his life, and he's finally dressing like the uber-wealthy tech mogul that he is. This fashionable outfit is Exhibit A on that.

Consider what he looked like when he first started Amazon in the '90s .. a stark difference.

Now, homeboy's in his Lex Luthor phase ... and he's definitely living it big as one of the richest men on the planet. Luckily for him, Lauren completely complements that vibe too.

They've been on a nonstop unofficial honeymoon ever since they got together -- traveling the world and soaking in vacays everywhere you can imagine. Safe to say, she's brought him out of his shell a bit ... or dare we say, his cocoon!