Born in the village of Glozhene, Lovech Province, Hubchev initially began his career as a central defender at Osam Lovech (today Litex Lovech) and being called up for the national team while still playing in B PFG. He was subsequently bought by Levski Sofia in 1989 after 249 matches for Osam. He stayed in Sofia until 1994, winning two titles and two national cups. His success during the 1994 World Cup meant he moved to German club Hamburger SV, a team he even captained. He then played for Eintracht Frankfurt since 1997, where he finished his career at the age of 38 and continued as an assistant manager and reserves manager, having played 128 matches and scored two goals in the German Bundesliga, as well as 44 matches in the 2. Bundesliga with another two goals.
In 2002, Hubchev became the assistant manager of the Bulgarian national team under head coach Plamen Markov, and he helped Bulgaria qualify for the Euro 2004 tournament. He continued as an assistant manager under new Bulgaria national team manager Hristo Stoichkov, and also briefly worked as Slavia Sofia manager in 2005. From the summer of 2009 he is manager of Chernomorets Pomorie. Houbchev managed the team to the final of the Bulgarian Cup by eliminating Minyor Pernik with 2–0 in the quarter-finals and Kaliakra Kavarna (4–1 after penalties). Chernomorets' players are the second ones from a B PFG team in the Bulgarian Cup history that have reached the final of the competition since Chernomorets Burgas's similar achievement in 1989. Chernomorets Pomorie lost 1–0 the final against Beroe with a late goal scored by Doncho Atanasov. In 2011 he was appointed manager of Botev Plovdiv, but was released after disappointing results. In January 2012, he was appointed director of sport at Beroe Stara Zagora. In October 2012, Houbchev became manager of Beroe.