The Spanish club said on their website on Monday that the 24-year-old had agreed a four-year contract.
They also confirmed the arrival of France midfielder Josuha Guilavogui from St Etienne on a five-year deal, which had already been announced by the Ligue 1 side.
"I wanted to sign for one of the best clubs in Europe," Atletico quoted Alderweireld, who will join international team mate and goalkeeper Thibaut Courtois at the club, as saying.
"He (Courtois) told me about Atletico's interest and how fantastic the team and their fans are. He recommended I come because he is very happy here."