Slim Shady is officially grandpa Shady ... 'cause Eminem's daughter Hailie Jade has welcomed her first child!

Hailie made the announcement on Friday ... posting to Instagram snaps of her little boy, Elliot Marshall McClintock, who was born March 14, with the caption, "happy due date//3 weeks earthside little e."

As you know ... HJ -- a major social influencer in her own right -- is one of Eminem's three kids with ex-wife Kim Scott -- and she's married to Evan McClintock.

As we reported ... Eminem revealed Hailie is pregnant last year in a new music video -- with his daughter giving him a custom Detroit Lions jersey with "Grandpa" on the back.

Hailie also gave her famous father a sonogram image of the baby inside the womb ... and Em looked pretty shocked.

Hailie and Evan married last May ... and have been together since 2016.

As we reported ... 50 Cent, Dr. Dre and Jimmy Iovine were among the guests at Hailie Jade Scott's nuptials.

It's a good bet Grandpappy Slim will lose himself spoiling the little tike rotten.