The youngster has signed an 18-month contract at Molineux.
The winger has signed an 18-month contract with the Championship side. The deal includes an option for a further year for the youngster who, according to the club's official website, was previously being monitored by Premier League sides.
Randall admitted upon signing that he was taken aback by what the club offered, and explained that he felt a move to Molineux was the right switch for him.
"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," he told the club's official website.
The 18-year-old will initially join up with Wolves' under-21 squad (via the club's official website), but Kenny Jackett will take some confidence from the fact that he had begun to make an impression as part of the Robins' first-team before his move. He made six appearances for Swindon this season, including four games in League One.
With Wolves in the top-half of the Championship, he will be hoping that he can soon make some kind of impact for his new club that can help take them into the promotion mix.