"It's a very pleasant victory," said McGeechan, after the Lions outscored the world champions by three tries to nil at Coca Cola Park.
"It's great to be going home with one. This victory lasts for four years."
The Lions arrived in South Africa's largest city on the back of two heartbreaking defeats in the opening two internationals and McGeechan admitted that there was always a danger that the players would be unable to get over those disappointments in time for the third and final rubber.
But that proved to be an unnecessary worry as his side outplayed the South Africans to ensure the Boks suffered their first defeat in Johannesburg since 2001 and ensure the Lions could leave the Republic for some sort of reward for six weeks of outstanding effort.
"The dressing room last week was one I never wanted to be in, so to come to this week and to play like that shows they're an outstanding group of players," added McGeechan.
"I was worried that they wouldn't play or might go into their shells a bit but we didn't and we scored some very good tries today.
"To be fair to the players, they've come here today with a real intent and a real focus and I'm just delighted that all the support that has been here had something to smile about and cheer about.
"We've tried to be careful in what we've done this week but everybody's had the same focus and that's been the same throughout the tour. That's been very important. The fact that we can still play like we did despite having to make so many changes shows how well the players have all integrated into the whole environment.
"I think it will be my last Lions involvement and I'd like to thank the players - they've been outstanding to a man."