In Veszprém there was a long tradition of handball, and in 1970 the Bakony Chemist TC women's team won the first championship among the rural ensembles.

The sports club was founded in 1977 under the wing of the Veszprém County State Construction Company (VÁÉV) under the name Of Veszprém Builders, after a political decision was taken in the city, which urged the men's division of BVTC, which had been relegated from NB II, to be taken over by the VÁÉV.

Over the next four years, the team won only four silver medals (three times at the Rába ETO, 1990–1992 Bramac, Fotex until 2005, MKB until 2015, MVM until 2016, Telekom-backed team since 2016: since 1992, 23 seasons, 20 championship gold and 3 silver medals have been awarded to Veszprém.

In April 2020, fans voted for the All Star team in club history, which includes Árpád Sterbik, Gergő Iváncsik, Carlos Pérez, József Éles, László Nagy, Mirza Džomba and Andreas Nilsson.

In 2024 they had four captains: Ludovic Fabregas (EHF Champions League) Patrik Ligetvári (K&H liga) Gasper Marguc (Hungarian Cup) Nedim Remili (Club World Cup) The following table shows in detail Veszprém KC kit manufacturers and shirt sponsors by year: