9:36 AM PT -- Sources close tell us baby #4 was born Thursday and weighed 6 lb. 9 oz.

5/10 9:05 AM PT -- The new baby West has arrived. Kim just tweeted, "He's here and he's perfect!" She continued, "He's also Chicago's twin lol I'm sure he will change a lot but now he looks just like her."

Kanye West and Kim Kardashian are about to be the proud parents of a brand spankin' new baby boy -- their surrogate's in labor!!!

Kourtney and Kris Jenner taped an episode of 'Ellen' Thursday with all of the Kardashian kids ... including Kim and Kanye's. Kourtney acknowledged Kim was supposed to be on the show but couldn't make it because there were urgent matters to attend to ... i.e., labor! And, get this, we're told Kris didn't even know.

Our sources say Mom and Dad were at the hospital Thursday night with the surrogate. Don't know for sure if they'll be in the delivery room, but she was the last time around for the birth of Chicago.

As we reported ... KW and KK hired a new surrogate to carry their fourth kid to term -- not because they were dissatisfied with the last one ... she was simply unavailable. The woman -- who was in her early 20s -- had her own child this past December ... less than 12 months after popping out baby Chicago. As a result ... the couple had to go with another surrogate.

This new surrogate's profile never became clear ... but ya gotta imagine Mom and Dad went with someone who was equally capable.

Kim and Kanye used a leftover embryo they created to bring this newest baby to life. He'll join three siblings -- North, Saint and Chi -- as the sixth member of the family.

As you know ... Kim's got a full plate. Aside from studying to become a lawyer and running of beauty empire, she's dedicating much of her time to prison reform, helping first free Alice Marie Johnson and Matthew Charles. Just last week, she helped free a man given a life sentence.

We'll keep ya posted on when baby #4 pops out ... but here's an early CONGRATS!!!