Mr Lux, who represents the French clubs on the ERC Board, has already been chairman for four years, taking over from the inaugural chairman, Tom Kiernan of Ireland, who served between 1995-1999.
A 57-year-old Dax dentist, Mr Lux won 47 caps for France as a centre between 1967-75 and also serves on the Ligue Nationale de Rugby, the body that governs the professional clubs in France.
"I was delighted to be asked to stand as chairman with the support of all the directors and I know that I can count on the wholehearted backing of the ERC Board once again over the next two years," said Mr Lux, who joined the ERC Board prior to the 1998/99 tournaments.
"One of the major reasons I decided to put my name forward for a third term is that much remains to be done to continue the excellent development of the tournaments governed by ERC and by the company itself. Gates are up, standards are improving both on and off the field and there is a genuine feeling that ERC has created something very special for the game in the northern hemisphere.
"There are exciting times ahead for all our tournaments and we are working very hard to complete new commercial and broadcasting contracts that will secure a bright and healthy future for the professional clubs across Europe.
"As we approach an historic moment in the Heineken Cup, with the first final featuring two teams from the same country, I am honoured to be representing the French clubs at a time when the trophy is due to head back to France for the first time in six years when Perpignan meet Toulouse in the final at Lansdowne Road, Dublin on 24 May."
Mr Lux's re-appointment will also allow him to oversee the 10th anniversary of the launch of ERC and the Heineken Cup in 1995.