The 32-year-old women's G.O.A.T. made the announcement on social media, saying ... "Speechless ❤️ Raegan Ann Nunes 9/24/2020 7:15 am #happydaughtersday #love #mylittlefamily"

Reagan was born Thursday morning in a Florida hospital.

34-year-old Ansaroff -- the #5 ranked UFC strawweight -- posted their very first family photo, and wrote ... "I am so in love! I can’t wait to show you the world! 💕💕💕💕💕💕💕💕💕💕💕💕💕September 24th 2020"

So, how's the couple doing?? We just talked to Dana White -- who was preparing for UFC 253 from Fight Island in Abu Dhabi -- and he told us the new moms are ECSTATIC!

The UFC honcho -- and father of 3 -- shared a photo sent by Nunes ... along with some parenting advice for the couple.

Now, the question is ... when does Nina -- who has won 4 of her last 5 fights -- return to the Octagon?

In June, Ansaroff told us she only wanted to take off 6 months after giving birth ... while Amanda wanted her fiancee to sit out a little longer!

A quick return to the Octagon isn't impossible. Remember, Mackenzie Dern fought only 4 months after giving birth to her daughter.