Shaw's departure from Bristol had been widely expected and Leicester were interested in the mobile 6ft 9in second-row forward until they switched their attentions to the Springbok Fritz van Heerden.
The way was left open for Nigel Melville, the former England scrum-half and director of coaching at the league champions, to present the 24-year- old Shaw with a three-year deal worth six figures.
Shaw's departure is a severe blow to Bristol, who survived the inaugural professional season in Courage League One, but may find life a lot tougher when the renamed Allied Dunbar Premiership starts on 23 August.
Given the number of casualties dropping out of the Lions tour, the ball- winning Shaw has has every chance of playing in one of the three Tests against South Africa.
Leicester's new boy, van Heerden, has been dropped for Saturday's first Test, but that will not affect how he is regarded at Welford Road. The club see the 26-year-old 6ft 7in Western Province lock as the perfect partner for the Lions captain Martin Johnson.
Leicester recently swelled their overseas contingent by recruiting the Fijian pair Waisale Serevi and Marika Vunibaka, underlining coach Bob Dwyer's determination that the Tigers should build the strongest possible squad.
Leicester were one of three clubs rejected by the Argentinian international Agustin Pichot in favour of newly-promoted Richmond. The 22-year-old scrum half, who also turned down Bath and Saracens, said he had been swayed in his decision by having stayed in the Richmond area.Reuse content