Lil Xan Says GF Only 5 Weeks Pregnant, But They Couldn't Wait to Announce

Lil Xan and his GF refuse to bow to old traditions ... which is why they announced she's expecting their first child, even though she's only 5 weeks pregnant.

The rapper and Annie Smith told us ... initially, they wanted to wait to share the news, but Xan was so overcome with joy he couldn't keep the secret. Typically, expectant parents wait until the end of the first trimester, just to make sure the pregnancy's going smoothly.

Xan says he cried tears of joy after Annie surprised him with her at-home pregnancy test results, and it all came pouring out Sunday night on the Internet. Turns out, Annie and the 22-year-old rapper had been trying to get pregnant but were still shocked they pulled it off.

They also aren't shy about what they want -- it's a boy ... they hope.

Check out the vid ... Xan -- who left a rehab facility in December and finished his treatment at home last month -- says he's motivated now, more than ever, with a little one on the way.

Congrats!!!