The Belgian defender had been long linked with a departure from the reigning Eredivisie champions and, despite reported interest from the Premier League, he has now moved to Spain.
And, after completing the deal, he told the club's official website: "I wanted to play for one of the best clubs in Europe. I am happy to be part of this club."
Alderweireld joined Ajax's academy from Germinal Beerschot in 2004 and went on to make his first-team debut in January 2009.
He has since made over 100 league appearances for the Dutch club, winning three Eredivisie titles and one KNVB Cup under the tutelage of Frank de Boer.
The 24-year-old has also been a regular fixture in the Belgian national team since making his debut at senior evel against the Czech Republic in 2009.
Atletico Madrid, who finished third in the Spanish top flight last season, also announced the signing of French midfielder Josuha Guilavogui from Saint-Etienne on Monday.
