The former FC Zorya Luhansk goalkeeper comes in on a six year deal and is the first signing of the Lopetegui era.
Florentino Perez has been determined to strengthen the Real Madrid squad this summer, and it's understood that Andriy Lunin is already in the Spanish capital ahead of his transfer to Los Blancos.
Marca report a further £3.5m will go to the Ukrainian side dependent on Lunin's performance at the Bernabeu.
Liverpool FC look set to miss out on Brazil international Alisson Becker, too, after the AS Roma goalkeeper was reported to have agreed terms with Real Madrid.
"Thank you, Andriy! Good luck in the new club!"
The 19-year-old had attracted interest from clubs such as Liverpool, Juventus and Inter, but ultimately signed for the Champions League title-holders.
Trump amenaza con imponer aranceles a autos importados de la UE
Beijing ha prometido tomar represalias con aranceles sobre la soya y otros productos agrícolas estadounidenses . El gobierno chino replicó anunciando represalias equivalentes contra productos estadounidenses .
Monchi has been busy throughout the summer to this point with Justin Kluivert, Ante Coric, Bryan Cristante and Ivan Marcano all joining the Giallorossi, although the Spanish Director of Football has admitted that sales are necessary if the club is to meet FFP rules.
"Real is my favourite team", he said.
Zorya subsequently finished fourth in the Ukrainian top flight and also featured in the Europa League group stage.
"We thank Andriy Lunin for his efforts for Zorya", the Ukrainian club said in a statement.
The same article states that the 6ft 3ins shot stopper is desperate to complete a move to Real Madrid as opposed to Premier League side Liverpool FC.