Rihanna and A$AP Rocky are officially parents ... welcoming a baby boy to the world.

Rihanna Gives Birth to Baby Boy

That's right, it's the couple's first kid together -- sources with direct knowledge tell us he was born on May 13 in Los Angeles -- but we don't yet know his name.

In January, the couple announced they were expecting -- with an NYC photoshoot -- both sets of fans went nuts with excitement for RiRi and A$AP.

While Rihanna looked stunning throughout her pregnancy ... wearing designer looks and proudly showing off her baby bump, some drama went down.

As we reported, A$AP was arrested just last month in a surprise bust as the couple's private plane touched down at LAX. Law enforcement sources told us the statute connected to an incident where Rocky is accused of firing shots at an acquaintance, grazing his hand.