There have been moments in the life and times of Gareth Bale when the odds that were massed against him simply seemed too great. At 15, despite his prodigy status, he stood at 5ft 4in and was surely too small, too spindly. At 18, in the year of his transfer from Southampton to Tottenham Hotspur, he damaged the ligaments in his right ankle; he needed two operations, the insertion of a metal pin and eight months on the sidelines. The complications threatened his career.

Then, there was the thing about the jinx, which was only four years ago. In 24 Premier League appearances for Tottenham, Bale had failed to taste victory and Harry Redknapp, the club's manager at the time, was so keen to chase the monkey from his back that he brought him on as an 85th-minute substitute at home to Burnley, with the team 4-0 up. Redknapp later joked that he was nervous about doing so. Tottenham won 5-0.

Redknapp was open to selling Bale and there was the sense that the boy from Cardiff was a little bit too soft. Redknapp said he felt Bale would limp off in training "if he got a little mark on him", while an incident involving an alice band and a late tackle seemed to sum up things. Bale went down but, as he had treatment, he could be seen feeling about for the band that upholstered his long hair. Redknapp was unimpressed, the pair had a chat and Bale tells the story against himself.

"It was something that probably needed to be said to me," he told the Guardian three years ago. "The gaffer had just arrived [in October 2008] and at the time, we were at the bottom of the league. I definitely needed to toughen up but that just comes with growing up."

Look at Bale now. The Premier League's best player from last season has become a Real Madrid galáctico; the most expensive signing in football history; a phenomenon in the making. When Cristiano Ronaldo became the previous record transfer in 2009, swapping Manchester United for Real in an £80m deal, he was already outstanding. Look at him now. Bale can see the path to greatness.

The nerves and excitement will churn when he is unveiled at Real; when he wears the club's colours for the first time; when he has his first training session. Every professional has a first-day story – and they tend to involve fiery baptisms of some sort. Take Dwight Yorke, on his first session at United. "Roy Keane blasted the ball at me from six yards and glared at me," Yorke recalls. "He said to me: 'Cantona would have controlled that.'"

Bale will have to earn his spurs at Real, where ego and strutting attitude underpin the ability. They know that they are special. Standards are intimidatingly high but Bale will not be fazed. In his down-to-earth way, he knows that he is special and he has always backed himself to rise to challenges.

Bale has grown. He has toughened up. As a primary schoolboy, he was the runner-up over 50m at the Welsh national under-11s championship. He has always been quick but when he experienced a rapid growth spurt at 15 he was discombobulated. He adjusted.

The ankle injury in December 2007 left its scars and it has resulted in Bale becoming fastidious about his physical preparations. Everything must be in tune. He looks after himself, he does not drink and his massive upper body these days is the result of hard work in the gym and with the Tottenham sports science team. Bale is an imposing figure, who strips big, as the pros like to say.

Bale listens. He had a haircut after his chat with Redknapp, for example, but what has long driven him is the single-mindedness that lurks beneath the unassuming smile and the Cardiff home-bird persona. He says that he gets it from his parents, Frank and Debbie.

The determination to succeed is intense and it has fired him to improve his game. There is a reason why his free-kicks, which swerve the wrong way for a left-footer, are so deadly. He has practised and practised. It has also why he has pushed for the move to Real, which holds no fears for him. Bale left home at 15 to join the Southampton academy. He is no shrinking violet; no dressing-room wallflower.

Is he good enough for Real? There are those that consider him to be an off-the-cuff player, who relies too heavily on pace and power, and lacks the sophistication to prosper in the more tactical Spanish league. The positive reading, though, is that he will adapt and become better. He is already the complete Premier League package, able to play anywhere on the left, as a No10 or inside-out off the right. And he has shown the capacity to tear apart European teams, after announcing himself on the Champions League stage with his performances against Internazionale in 2010-11.

Tottenham could not say no to Real. Never mind Bale's desire to leave in order to experience regular Champions League football and compete for the biggest prizes, the money on offer was just too persuasive.

The challenge for the chairman, Daniel Levy, and the manager, André Villas-Boas – as it was last summer when they sold the club's best player at the time, Luka Modric, to Real – has been to finesse the transfer market and make the squad collectively stronger. It can be argued that they succeeded last time out as Villas-Boas's remoulded team finished the season with a record Premier League points tally and a Europa League campaign to be proud of. Bale, however, was the key. Previously excellent, he reached new levels and frequently found the way to be decisive.

A club can surely not lose the country's most destructive player and become stronger but Tottenham have succeeded in demonstrating ambition and exciting their supporters. There is still the sense of momentum at White Hart Lane, of dynamism, of a club having a proper go.

Villas-Boas has been permitted to shape a team in his image and he has invested, at great cost, in highly technical European and South American players. They are unproven in the Premier League but Roberto Soldado already looks accomplished and there is verve in behind the new centre-forward, where Paulinho is an eye-catching midfield addition. The loss of Willian to Chelsea was a blow but the expected arrival of Erik Lamela should soften it. Villas-Boas wants two players for every position and he now boasts formidable depth.

Tottenham continue to be optimistic. Bale's journey has taken him closer to the stars.