Watkins, a prominent sports lawyer and senior non-executive director of the RFL, will hold the reins until a new chairman is appointed to succeed Lewis, a former Davis Cup player who is leaving after 10 years at the helm to become chief executive of Wimbledon.
Watkins said: "I will be working with my board colleagues to identify the skills we require for a new chairman to take the game on to the next exciting stage of its development."
He added: "At the same time we will take this opportunity to review the game's governance arrangements for the next era, in consultation with all our stakeholders.
"Whilst tough economic conditions are proving challenging for all sports clubs at present, we believe this is a great moment for someone to come in and help shape the future of a very successful sport."
Lewis took over from Sir Rodney Walker in May 2002 with the governing body in debt to the tune of £1.9million, partly due to a disastrous 2000 World Cup, and oversaw a swift improvement in their financial fortunes.
He also helped to unify the domestic game, bringing all the different sections under one roof, and raised the profile of the worldwide game in his role of RL International Federation vice-chairman and European Federation chairman.
RFL chief executive Nigel Wood, who joined the administration in 2007, said: "It is my firm belief that history will record Richard's stewardship of rugby league as a golden decade for the sport where considerable progress was achieved across all fronts.
"He brought integrity, independence and credibility to everything he and the RFL did, and he leaves safe in the knowledge that the sport is undeniably in a far better condition than when he joined in 2002."
Lewis, 57, said: "I leave the RFL after 10 fulfilling years during which the sport has grown and prospered. Rugby league is a wonderful sport full of great people in both the professional and community games. I have enjoyed tremendous support during my tenure, from the board, colleagues at the RFL and throughout the sport in general."