Struggles at Santiago Bernabeu had seen a move mooted for some time, with Zinedine Zidane taking to freezing Bale out of his plans.
China, MLS and Old Trafford were considered to be possible landing spots, with Premier League heavyweights reported to have rekindled their interest this summer.
Spurs, though, have won the race for a much sought-after signature and re-signed Bale on an initial season-long loan.
Quizzed by BBC Sport on how that agreement came about, with others left empty-handed, Barnett said: “Basically it was a conversation between [Tottenham chairman] Daniel Levy and myself where the subject came up, I suggested it and Daniel was interested.
“So that's basically how it was done. No magic, just long chats.
“Daniel Levy's been interested in bringing Gareth back for a long time. There was always a reason why it couldn't happen. Just this was the right moment.
“They made the move first.”
Bale is looking forward to opening a second stint with Spurs, having previously left as the most expensive player on the planet in 2013, and Barnett believes an extended stay could be earned.
He added: “I'm sure that if things really worked out well, we'd have no problem.
“This is the club he wants to play at. I don't see any problems if he wants another year.”
Pressed on the chances of a return to Madrid being made, with Bale still under contract until 2022, Barnett said: “Hopefully the subject won't come up. He will be so successful at Tottenham he'll want to stay and it will be a simple deal to do the rest.
“What I hope is he'll get his love back for the game and play the way he can, but it's up to him.
“And he's not on trial anywhere. He's achieved more than any other, I think, British footballer abroad, so I think he's fine.”
While becoming a scapegoat for some in Spain, Bale has won 13 trophies with Real – including two La Liga titles and four Champions League crowns – and Barnett claims he has been unfairly treated given all that he has achieved.
“In my opinion, he wasn't treated correctly for somebody who's done so much for a great club. I think that things were wrong,” he said.
“It's hard to put one finger on it but I think somebody who has achieved what he has achieved for a club, in seven years, should have been treated better.
“I don't want to blame anybody or go into it. I think what the fans did was disgraceful and the club didn't help. That's all I really want to get into.”
Spurs are hoping that Bale can shake off a knee injury to figure for them before the next international break in October, with Jose Mourinho confident that a speedy recovery will be made.