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: Paul Pogba posts cryptic message on Instagram after Manchester United win
More news: 30 killed, over 50,000 homeless as heavy rains continue across Kerala
More news: England name squad for second Test against India
"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.