He joined the club on a four-year deal from Aston Villa in 2016, having signed from Barcelona the year before.
Manchester City youngster Zinchenko was the club's initial target, but the reigning champions refused to part company with the 21-year-old.
He scored five goals and provided 10 assists in the previous campaign in the second-tier Championship to be voted Middlesbrough's player of the season.More news: Judge orders plane carrying deported mother, daughter to turn around
More news: Which men's underwear is best for healthy sperm? Science finds the answer
More news: Nasa counts down to launch of first spacecraft to 'touch Sun'
"I hope the supporters understand both players in respect of their decisions to play in the Premier League".
"I like to work hard and push myself every day". Although the Ukrainian worldwide would have beefed up their arsenal further, they still have a formidable side to ply their trade in the Premier League.
Wolves have agreed a deal in principle with City for Ukrainian utility man Zinchenko - who could play at left wing back or central midfield.
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.