It is understood the Belgium defender, 26, has completed a medical and agreed personal terms at Spurs after their chairman Daniel Levy spent the weekend in Madrid agreeing a deal to bring him to White Hart Lane.
The north London club are pressing ahead with the move despite Southampton, where Alderweireld spent last season on loan, considering legal action against Atletico for doing a deal with another club.
Saints had a £6.8m agreement in place to make his loan permanent, which Atletico had to pay £1.5m to buy themselves and the player out of, and it is understood the Spanish club did not do so within a time-frame previously agreed between the two clubs.
Sky Sports reported last week that Spurs had made Alderweireld one of their top targets this summer and were determined to make him a Tottenham player as Mauricio Pochettino bolsters last season’s leaky defence.
Alderweireld played 26 times as Southampton conceded 20 fewer goals in the Premier League than Spurs last season, having failed to establish himself in Atletico’s first team.
He moved to Madrid from Ajax, where he also played with Jan Vertonghen and Tottenham forward Christian Eriksen, in 2013, but only started 10 times as Atletico won La Liga in 2013/14.
Born in Antwerp, Alderweireld was an Ajax academy graduate who played over 100 games for the club and won the Eredivisie three times between 2011 to 2013. He has 47 caps for Belgium.