Schmidt stood down from the role to spend more time with his family in New Zealand.
Davies, a 45-cap Test veteran, took Namibia to the 2015 and 2019 Rugby World Cups. Het has also been a head coach for the Cardiff Blues, Scarlets and Leeds.
Davies starts in the role this month.
He has an agenda of shaping performance management processes for elite match officials, nurturing relationships with high-performance national team coaches while also advancing World Rugby's relationship with players on performance matters.
He will also be involved in supporting emerging nations in making a lasting bridge between them and those countries at the highest levels of the game. He will also ensure player welfare retains its place in the law review process.
Davies said he was looking forward to getting started.
"I am passionate about the sport, its people and global potential, and I believe that I can bring my experiences of playing and coaching in more than 20 nations over the past 35 years, to support further growth and development to the sport, both off and on the field, in particular in the important areas of welfare, sustainable high-performance programmes and laws evolution," he said.
World Rugby chief executive Alan Gilpin said: "Phil's profound knowledge and passion for the high performance and technical aspects of the game, couple with the huge respect that he carries, will help us build on solid foundations forged by Joe Schmidt to increase our connection and collaboration with important stakeholders – players, coaches, match officials and fans."