Murphy has made more than 250 Tigers appearances and is the club's all-time leading Heineken Cup try-scorer.
"It is a great honour to lead out such a great club, but there is so much experience and so much quality around the playing squad that it allows you to get on with your own game and trust the rest of the guys to do the same," said Murphy.
"Like all of the guys, I'm looking forward to the start of the season, to two big away games against Sale Sharks and Harlequins, and then to the return to Welford Road and hopefully a capacity 24,000 crowd for the first home game against Newcastle Falcons."
Murphy follows in the footsteps of another Test Lion, England back row man Martin Corry. All Black Aaron Mauger and England international Louis Deacon have been appointed vice captains for the forthcoming campaign.
Tigers head coach Richard Cockerill said: "Geordan has been at Tigers for more than a decade and has been a fantastic servant to this club. He was captain at the end of last year and did a fantastic job.
"The way we want to play and the way we want to improve our game is with ball in hand and Geordan epitomises that.
"He has the respect of the rest of the squad and I wanted someone who is integral to Leicester Tigers, which he is."