Ohio State QB Braxton Miller -- Undergoes Shoulder Surgery ... LeBron Sends Well-Wishes

Ohio State QB Braxton Miller is out of shoulder surgery -- after a season-ending injury to his labrum last week -- and woke up to a get-well note from LeBron James.

Miller -- who was considered one of the top college QBs in the country -- hurt himself during football practice ... and scheduled a surgery with legendary orthopedic doc James Andrews who has famously worked on huge stars like Tom Brady, Drew Brees and even Bo Jackson.

“Me & the best to do it , Dr. Andrews after surgery today," Miller wrote on Instagram ... adding, "So happy this man said everything went well!"

As for LeBron -- he went to Instagram to send some love to his fellow Ohioan ... writing, "Excited and Happy my lil bro @braxtonmiller92 surgery went great! Thanks to the best Dr. Andrews!"

Bron continued, "You'll be better than ever. Have a speedy and full recovery bro. See you soon! #GoBucks #OH #IO"