"He has been invaluable to my progress in the last two or three seasons," said the 21-year-old fly-half, who was instrumental in Wasps' charge to the Guinness Premiership title in 2007.
"He has a lot of wise words and we learned a lot from him."
McGeechan and Cipriani may not have enjoyed such a successful season this time around in terms of results but the young England star believes he has continued to learn and to improve under the stewardship of McGeechan and fellow Lions coach Shaun Edwards.
"It was a difficult season at first but in the last 10-12 games of the season myself and the club were coming into form," added Cipriani.
"I have been happy with the coaches at the club and I have learned loads."
Cipriani has made himself available for England's series against Argentina and the Lions tour of South Africa if he is required after choosing to wait until the international season comes to an end before having a pin removed from his ankle.