With Matt O’Connor moving on to become head coach of Leinster after this year’s Aviva Premiership Final, Burke becomes backs coach with former club captain Murphy as assistant backs coach.
They will both work alongside director of rugby Richard Cockerill and assistant forwards coach Richard Blaze.
Cockerill said: “Matt O’Connor has done a fantastic job in his five years with the club and we are sorry to see him leave. He has worked extremely hard for the club and I’m sure he will do a very good job at Leinster. We wish him well.
“Paul Burke has been learning his job as an assistant coach over the last five years here and has done a very good job. He is very experienced in the game in a number of different environments and we see this as an opportunity for him to make his own mark on the team.
“Geordan obviously knows Leicester Tigers very well, he knows and understands the game at the very highest level and has a wealth of experience and knowledge to pass on to others. He has enjoyed a very successful and lengthy playing career and we believe he can become a top-class coach.
“By bringing Paul and Geordan together in the coaching team we have a degree of continuity which I feel is very important in our environment and we look forward to seeing their continued development in their new roles.
“Richard Blaze has done an excellent job on the coaching side since he had to retire as a player at a very young age. He works very hard at his facets of the game and continues to develop and improve all the time.
“As coaches we all bring different things to the table and it is important to have a strong coaching team who all work together and all have an input because there is a lot of work to get through in a long and tough season.”
