Jenkins was dismissed on Sunday morning after Wales crashed out of the World Cup with a 38-34 defeat by Fiji.
The WRU board met on Tuesday and decided the successful candidate will be awarded a four-year contract through to the 2011 World Cup.
The coaching staff who worked under Jenkins at the World Cup - Nigel Davies, Rowland Phillips, Robin McBryde and Neil Jenkins - will remain in place to prepare the team for November international against South Africa.
A caretaker head coach will be appointed for the game in due course.
Lewis said: "Today we fully debriefed the WRU board on the events of the weekend surrounding the departure of Gareth Jenkins.
"There was a full and detailed discussion about what we must now do and that includes a full review of all aspects of elite rugby in Wales.
"The task of finding a new head coach is now our priority and has started in earnest this evening."
Nick Mallett, Eddie Jones and Mike Ruddock have already indicated they are not interested in the post.
Others to have been linked with the position are Scott Johnson, a member of Ruddock's coaching staff during the 2005 Grand Slam, Crusaders coach Robbie Deans and Llanelli Scarlets boss Phil Davies.