Gheorghe Dogărescu began playing handball at his local sports school before representing Dinamo București from 1979 to 1995. With the club Dogărescu won the Romanian title and finished second in the final of the 1982–83 EHF Cup Winners’ Cup. He was first selected to represent the Romanian junior team in 1977 and won the Latin Countries Cup in 1981. That same year he made his senior début for the national team, playing for them until 1990. In 1984 Dogărescu was part of the Romanian squad that won bronze at the Los Angeles Olympics after beating Denmark 23–19. He continued to have success with the team, winning gold at the World University Games in 1985 and 1987.