The fee has not been revealed by either Real or Tottenham, but it is tipped to be a world record, surpassing the £80million spent by Real when they signed Cristiano Ronaldo in 2009.
The transfer represents a significant step in the 24-year-old's already outstanding career and here we look back at Bale's life in football, tracking his meteoric rise from talented teenager to international superstar...
1989: Bale is born in Cardiff on July 16, to parents Frank and Debbie. Football is in Bale's blood from birth, with his uncle, Chris Pike, a former Cardiff City player.
1997: He is spotted as an eight-year-old while playing for a Cardiff Civil Service side. Bale impresses Rod Ruddick - involved in Southampton's academy - at a football tournament in Newport. He begins training sessions at the club's satellite academy in Bath shortly after.
2003: Bale is reported to have run the 100m sprint in 11.4 seconds at school at the age of 14, when he also begins travelling to Southampton for training.
2005: He joins Southampton officially, signing trainee terms with the club.
2006: April 17 - The Welshman becomes the second-youngest player to ever represent Southampton in a 2-0 win against Millwall, at the age of 16 years and 275 days. Only Theo Walcott (16 years, 143 days) was younger.
May 27: Bale becomes the youngest ever Welshman to play for the senior team, making his debut in a 2-1 friendly win against the Trinidad & Tobago in Austria. Aged 16 years and 315 days, Bale comes on as a substitute and provides the assist for Rob Earnshaw's late winner.
July 16: Turns 17 and marks the celebration with the signing of his first professional Southampton contract.
August 6: Scores a free-kick on the opening day of the 2006-07 season as Southampton draw 2-2 with Derby. The goal is Bale's first for the club.
September 5: A first Wales start follows in a 2-0 friendly defeat to Brazil at White Hart Lane.
October 7: The records continue to tumble as Bale becomes Wales' youngest-ever scorer when he nets a free-kick in a 5-1 loss to Slovakia in a Euro 2008 qualifier.
2007: March 4 - As part of an excellent season in the Championship for Southampton, in which he scored five goals from 38 appearances at left-back, Bale is crowned the Football League Young Player of the Year.
May 12: Bale limps off injured in Southampton's 2-1 loss to Derby County in the first leg of their play-off semi-final. They eventually lose in a penalty shootout, with the fixture at St. Mary's Stadium Bale's last as a Southampton player.
May 25: Tottenham agree an initial £5 million fee for Bale, potentially rising to £10 million dependent on future success. The player moves to White Hart Lane to continue his rise through British football.
July 12: Bale makes his Tottenham debut in a friendly against St Patrick's Athletic. Tottenham win 1-0.
August 26: A Premier League debut follows, with Bale stepping out in Tottenham's 1-0 loss to Manchester United.
September 1: Bale's first Premier League goal comes in a 3-3 draw at Fulham.
September 15: Tottenham fans take to Bale immediately, as he scores a free-kick in a 3-1 derby loss to rivals Arsenal.
December 2: Bale suffers a season-ending foot injury in a 3-2 defeat at Birmingham City.
2009: September 26 - After playing 24 Premier League matches without featuring in a win, Bale finally breaks an unwanted hoodoo, as he plays a part in Tottenham's 5-0 triumph against Burnley.
2010: May 7 - Bale signs a new four-year deal with Tottenham after helping them to a fourth-placed Premier League finish with a series of excellent performances.
October 20: The winger announces himself on the European stage, scoring an incredible hat-trick in a 4-3 UEFA Champions League defeat to Inter Milan at the San Siro.
November 2: Bale repeats the trick against Inter, starring in a 3-1 group-stage win at White Hart Lane.
2011: March 19 - Bale signs another contract with Tottenham, this time for a four-and-a-half year term.
2012: January 18 - Announced as a member of UEFA's Team of the Year for 2011.
June 27: After more impressive form, Bale signs a new four-year deal. It his third new contract in just over two years.
October 20: Bale's first child - daughter Alba Violet - is born, as the Welshman begins the season in outstanding form.
2013: February 7 - Tottenham manager Andre Villas-Boas admits the club are unlikely to keep Bale if they fail to qualify for the Champions League.
April 28: Bale wins the Player of the Year and Young Player of the Year at the PFA awards.
May 19: A goal on the final day of the Premier League season against Sunderland helps Tottenham to a 1-0 win. Bale finishes the campaign with 21 goals in 33 appearances but Spurs finish fifth and miss the Champions League spots.
August 22: After weeks of speculation linking Bale with a Real Madrid move, the Spanish club offers shirt printing with 'Bale 11' on the back on their official website.
August 28: Bale refuses to train at Tottenham for the second day in a row as Real Madrid's world-record bid for him apparently nears completion.
September 1: Bale's move to Real Madrid is finally confirmed, shortly after Tottenham lose 1-0 to Arsenal.
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