Bradley Cooper & Irina Shayk ... Finally Make It Official

Bradley Cooper and his supermodel girlfriend Irina Shayk aren't hiding their relationship anymore ... in fact, they're swapping spit for all to see.

Bradley and Irina finally made their red carpet debut as a couple Tuesday night at the L'Oreal Red Obsession Party in Paris.

It's been a long time coming ... they first began seeing each other last May, but tried to keep things on the hush hush.

Mazel.