Genvex A / S was founded by Bjarne R. Svendsen in 1978, when he bought the Climate Department from V.M Christensen and reshaped it into his own company – Genvex Klimateknik. Bjarne R. Svendsen was a former employee at V.M. Christensen from 1974-78, a time, where the oil crisis of ’73 had sparked an interest in the research and development of alternative energy sources. This was part of the reason why V.M Christensen – and later Genvex – developed and produced ventilations systems and domestic hot water heat pumps, as both product types were seen as possible solutions to the problems created by the oil crisis.

During the first years, Genvex primarily focused on developing ventilation systems with cross-exchangers (“passive” systems). But in 1980, Genvex A/S introduced the so-called "active" systems - ventilation systems with built-in heat pumps. In the following years, Genvex also started working on cooling systems, COMBI 185 series (systems with built-in hot water tank) and ventilation systems with larger capacity. Between 1980 and the early 90s, Genvex increased sales abroad, and sales to businesses and public institutions in Denmark also began to pick up.

In the year 2000, Genvex moved from Copenhagen to the current location in Haderslev in order to expand the production facilities. Four years later - in 2004, Genvex A / S is sold to the Swiss Schulthess Group, which a few earlier also had acquired Alpha Innotech and KKT in Germany. Genvex A/S is included in the Heating Technology Group within Schulthess Group.

In 2011, the Schultess Group is bought Swedish NIBE AB, where Genvex becomes a part of NIBE Energy Systems. As part of the acquisition, Genvex was also included in the METRO THERM group, and several of the departments in Genvex - including part of the management and marketing - is now run from METRO THERM's head quarters in North Zealand.

Shortly thereafter, Bjarne R. Svendsen retires from the company, and NIBE hires Michael Kanstrup Jensen as the new CEO

In 2014, Genvex A/S and KVM-Conheat A/S merged into a combined company called KVM-Genvex A/S. However, the two companies' products are still sold (2021) under their respective brands.