The 24-year-old had been linked with a number of sides during the close-season but opted to switch the Eredivisie for La Liga at the last minute following an enticing offer from Atletico.
His four-year deal with Diego Simeone's side marks only the first move of his career after spending the last five years with Ajax, where he came through the youth ranks.
Liverpool secured defensive additions in the shape of Tiago Ilori and Mamadou Sakho, leaving the Belgian content with his decision.
"The club have been following me now for two or three weeks, and you could see they really wanted me," he said.
"That is why I turned down approaches from other teams. Liverpool, for example, appeared in the last few days, but I had already taken my decision.
"The truth is that Atletico made a huge effort to convince me."
Ilori and Sakho, who arrived from Sporting Lisbon and Paris Saint-Germain respectively, helped to bring Brendan Rodgers' tally of new additions up to nine - with Chelsea star Victor Moses also completing a late loan move.
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