V.J. Edgecombe couldn't hold back the tears after the Sixers drafted him with the third overall pick in the NBA Draft ... crying on live TV as he thanked his mom for all her sacrifices -- and it was super sweet!

The star Bahamian athlete walked up on the Barclays Center's stage on Wednesday and shook commish Adam Silver's hand after Philadelphia pulled the trigger on the 6'5" guard.

Edgecombe's mom started the waterworks ... as she witnessed her son's dreams come true -- a moment that deeply moved V.J. during his post-draft interview with Taylor Rooks.

"That's what I'm here for. I know you seen the emotions on my momma's face," Edgecombe said. "She worked too hard, man. She worked too hard, especially for me, my brother, my little sisters, and my little brother. I just wanna return the favor."

"I lived off a generator. I had no electricity; I had to live off a generator for seven years. Seeing what she had to go through to feed us ... man, it's crazy."

Sixers executive Daryl Morey raved about Edgecombe following the draft ... calling the former Baylor standout a "potential All-Star."

"He's got all these winning qualities that we think really fit," Morey said.

"His story and what he's done to get to this point is really unbelievable and we think he's on a great trajectory to take where he's come from and really continue to improve through Baylor all the way through a very long and very promising NBA career and we're excited it's here with the 76ers."

Edgecombe moved from the Bahamas to the United States in the ninth grade to chase his NBA dreams ... eventually becoming a five-star high school recruit and a star for the Baylor Bears.