The 20-year-old defender has signed a five-year deal at the Vicente Calderon after completing a medical on Wednesday
The 20-year-old has been in the Danubio first team for two years and was part of Uruguay's preliminary World Cup squad. However, he is expected to earn his first cap with the national team against either Japan or South Korea in September.
Velazquez was among the best defenders in the Uruguayan Primera Division last season, with Danubio claiming the title for a fourth time.
Velazquez has already passed his medical and joins the Spanish champions on a five-year contract.
Atletico said in a statement on their website: "Atletico de Madrid and Danubio FC have reached an agreement for the transfer of Emiliano Velazquez (Montevideo, Uruguay, 1994).
"The Uruguayan underwent the relevant medical examination at Majadahonda's Fremap clinic before signing the contract that binds him to our club for the next five seasons."