Meek Mill I Slid into Tom Brady's DMs ... He Responded!!

Meek Mill fanboy'd HARD after congratulating Tom Brady on winning the Super Bowl ... 'cause the QB messaged him back with compliments of his own ... and the rapper is still geekin' about it!!

The Philly rapper detailed his private social media convo with TB12 while speaking at the MIT Sloan Sports Analytics Conference in Boston on Friday ... saying he reached out to Brady to praise him for being the GOAT.

But what happened next caught Meek by surprise, 'cause Brady responded -- praising the rapper's mental toughness through Meek's controversial stint at a Pennsylvania state prison.

"I didn't know Tom Brady knew who I was, I just took a shot, and he was like 'I seen you been thorough so much,'"…