The 18-year-old has joined Wolves on an 18-month contract for an undisclosed fee.
Randall will link up with Scott Sellars’ Wolves Under-21 squad.
Randall told the Wolves website: “This is a great move for me for the stage I am at in my career and my development.
“When I came here last Friday for the meeting and had a look around the facilities I was blown away by everything and by the plan the club have got for me.
“I think I can progress and improve my football here. I have been at Swindon’s Academy from the age of seven right through to now at 18 and have nothing but good things to say about them.
“I feel like I really improved during my time there and it was just that last hurdle – going from youth team to first team – that I had reached.
“I made my debut for Swindon the day after my 17th birthday and I have made a few more appearances since then which has been great experience for me.
“Playing in front of big crowds and getting that experience of men’s football will help me as I am to push on here at Wolves.”