Booth won two Premiership titles and helped Tigers claim back-to-back European Cup triumphs during his four years at Welford Road.
He went on to have a season with Premiership rivals Bath in 2005.
“Steve was a big personality in a dressing room full of big personalities,” said Murphy.
“He was a real entertainer on the pitch and will be remembered as someone who could score tries out of nothing.
“We were shocked to hear of his passing and, on behalf of everyone at Tigers, pass on condolences to his partner and their family and friends.”
Bath, as well as a number of his former team-mates, also posted a message of condolence on social media.
Booth, who played Rugby league for Huddersfield and Doncaster before switching Rugby codes to join Leicester in 2000, went on to work as part of BBC Radio Leicester’s commentary team and founded a digital design company after retiring as a player.