McGeechan will take charge for the fourth time having become synonymous with the Lions in an association as player and coach which stretches back through six tours and 34 years.
In 2005, McGeechan was in charge of the midweek team - the "dirt-trackers" - which travelled through New Zealand unbeaten while the Test team were humbled 3-0 by the All Blacks.
He left a lasting impression on Williams, whose only previous experience of McGeechan had been from watching the famous behind-the-scenes documentary of the victorious 1997 tour to South Africa.
"I got on very well with Geech, I thought he was great," said Williams. "There were times he stood up to deliver a speech and it was overwhelming. It made the hairs on the back of your neck stand up.
"Those team-talks and how he made me feel before going into games are the things I remember most about the tour. Motivationally he is one of the best you will come across.
"He is a very good speaker, he is a very good people person. He was one of the coaches I got on with most on tour and it is great he is involved again.
"He is a very experienced coach, manager, player. You name it, he has done it. He is an ambassador to the Lions."