The club secured the signing of Adama Traore from Middlesbrough for a club-record £20m on Wednesday to add to their early window additions.
"The 22-year-old completed his medical on Tuesday morning and put pen to paper on a five-year deal at Molineux", read a statement from Wolves on their website.
After taking a couple of seasons to click, the ex-Barcelona winger was largely unplayable in the Championship last season, terrifying defenders with his incisive running, jinky footwork and searing acceleration - scoring five goals and laying on 12 assists in the space of 40 appearances.
Sources said Wolves have reopened talks with Zinchenko's representatives and are optimistic of striking a deal to bring the Ukrainian worldwide to Molineux.
The Spain Under-21 worldwide moved to Aston Villa in 2015 but struggled with consistency before being left out of the side due to disciplinary issues as the Villains were relegated.
Nuno Espirito Santo's side will open their Premier League campaign at home to Everton on Saturday evening as they return to top flight action for the first time since suffering relegation in 2012-13.
The Spain Under-21 global joins fellow close-season recruits Rui Patricio, Jonny, Joao Moutinho and Raul Jimenez at Molineux with Wolves opening their top-flight campaign at home to Everton on Saturday.