In 1986, Cóceres turned professional and won a place on the European Tour at its 1990 Qualifying School.

After struggling in 1991 and 1992 he performed steadily on the tour from 1993 onwards and in 2000 he reached a career high of thirteenth on the Order of Merit.

His first season in the U.S. was very inconsistent, with seven missed cuts and only two top ten finishes, but those top ten finishes were wins at the WorldCom Classic - The Heritage of Golf and the National Car Rental Golf Classic Disney.

He was the first Argentine to win on the PGA Tour since Roberto De Vicenzo at the 1968 Houston Champions International.

In 2002 he became the third golfer to receive Argentina's highest sports award, the Olimpia de Oro ("Golden Olympia").