Born in Montevideo to Spanish parents, Santamaría played for local Club Nacional de Football in his country, winning five national championships during his spell. In 1957 the 28-year-old moved abroad, signing with Real Madrid where he remained until the end of his career.
In his first season with the Merengues, Santamaría contributed with 34 appearances the La Liga and European Cup tournaments combined, with both ending in conquest. He went on to add a further ten major trophies to his collection, being first-choice for the vast majority of his stint.
Having earned the nickname 'The Wall' for his consistent defensive displays, Santamaría retired at the end of the 1965–66 campaign at the age of nearly 39, featuring twice in that year's European Cupen route to another triumph (against Feyenoord and at Kilmarnock). He played 337 official games for Real Madrid.
Santamaría was first called up to play for Uruguay for the 1950 FIFA World Cup in Brazil, being selected to fill an inside forward slot in the squad but seeing the request denied by his club on the grounds that he was a defender. Four years later, however, he was an integral part of the national team setup at the World Cup in Switzerland, helping it to a final fourth position and gaining a total of 20 caps.
After working with the youth sides and spending two years with the under-21s, Santamaría was appointed manager of the full team for the 1982 World Cup, due to be played on home soil. He was relieved of his duties at the end of the competition, as Spain was unable to progress from the second group phase, and quit football altogether to pursue other interests.