He is appointed after an Elite Performance and Medical Review conducted last season and he takes up the position on Monday, 14 February.
He joins the Wales national set-up from his position as head physiotherapist of London Wasps, but first worked with the majority of the Wales national coaching team and a significant number of the players on the 2009 British & Irish Lions tour of South Africa.
Before joining Wasps in the summer of 2007, when he saw the club win the Guinness Premiership title in his first season, Mathema worked as a physiotherapist for Queens Park Rangers Football Club for eight years and during that time experienced a play-off final and promotion.
The 33-year-old career medical professional graduated from Brunel University in London and holds a BSc in Physiotherapy amongst a variety of other relevant qualifications.
"Prav made an impression on everyone on the Lions tour with his professional manner, his energy and his expertise," said Wales coach Warren Gatland.
"A number of the Welsh players built a close working relationship with Prav on that trip and he comes to us highly recommended from many sources and he will be an asset to the team."
Mathema said: "I'm really looking forward to the challenge of joining the WRU and working not just with the Welsh national squad but at all levels in Welsh rugby.
"My experiences on the 2009 British & Irish Lions tour was a really positive one and the Welsh players were probably the group I worked the most with and related to most.
"From that point of view I'm excited about working with what was a great bunch of players again and maintaining and developing the high standards of physiotherapy and medical treatment in Welsh rugby.