Mullen had been acting as Money's number two last season and the former Blackpool and Burnley boss has now been given the top job at the Bescot Stadium.
"We have had a number of interesting applicants, but Jimmy stood out as the right man for the job," said the Saddlers chairman Jeff Bonser.
"He has a wealth of experience, holds the highest possible coaching qualifications and has an inside working knowledge of the club.
"As you would expect, we had a large number of applicants for the position. From those applicants, a short-list of five was drawn up by the board, all of which were given serious consideration.
"After a number of formal meetings with all the prospective candidates, it was Jimmy who was the strongest candidate.
"He has a proven track record as a manager following a very successful spell at Burnley and, during his time here, has impressed everyone with his knowledge and passion for the game."