"As a coach in international rugby, one of the privileges is seeing great players emerge," McGeechan wrote.
"Players whose presence and performances change the way the game is played. Without doubt, Dan Carter is one of those.
"I will never forget his performance in the second Test of the 2005 Lions tour to New Zealand. He was supreme; the most complete No.10 the game had ever seen. And that was saying something.
"...the hallmark of a great player; the impact he has on those around him. Carter had that in spades.
"A great defender, he was brave, skilful, quick, a machine with the boot. To average 14 points a Test (he scored 1,598 points in 112 games) is remarkable, however good your team-mates are.
"And let us not kid ourselves, the All Blacks were, and remain, the greatest team in the world. Carter made them better. Even in the World Cup final in 2015, when he was near the end and hobbling around on one leg, he was instrumental in New Zealand winning."
Dan Carter still the hottest ticket in rugby
McGeechan recalled Carter's influence in that final.
"In the first half, he kept Australia pinned back on their own 22. And in the second, after Australia had closed to 21-17, he swung the game in New Zealand's favour," he wrote.
"He landed a dropped-goal he had no right to, to make it a seven-point game again. Then, from the kick-off, he produced a lovely chip from which he tackled Kurtley Beale, inducing a knock-on, a New Zealand scrum and then a penalty, which he converted from 51 metres: 27-17.
"In the space of three minutes, Carter had changed the momentum of the game almost single-handedly. Even then he made a fantastic tackle on the wing."
McGeechan believed England's Jonny Wilkinson was the nearest challenger to Carter.
He listed Barry John, Phil Bennett (Wales), John Rutherford, Gregor Townsend (Scotland), Michael Lynagh, Stephen Larkham (Australia), and Rob Andrew (England) as the other No.10 stars possessing "game-changing genius".
McGeechan said current All Black first five-eighths Beauden Barrett was "incredible in an attacking sense but I do not think he controls games as well as Carter did. He was found out a bit by the Lions last summer."
Carter will join the Kobe Steel-owned Steelers and while Japan is the next World Cup host, there is only minimal attention paid to club rugby in Japan.
