The deal, which is thought to be around £15 million plus add-ons, is currently being finalised by the two clubs.
Spurs have been keen to bolster their defence this summer after some mixed displays at the back last season. Davinson Sanchez and Eric Dier, amongst others, both went through difficult spells which meant Spurs struggled to achieve their targets for the season.
Tomiyasu is also capable of playing at right-back, where Spurs could soon be without Serge Aurier, and Belgian defender Toby Alderweireld has already told the club that he wants to move on this summer.
The Japanese defender would become the first signing since Fabio Paratici became Spurs’ managing director and since the arrival of Nuno Espirito Santo as the replacement for Jose Mourinho.
Despite other English clubs having an interest, Spurs have always been the first choice for Tomiyasu.
Manchester United were among those considering a move but he was never deemed to be a primary target for them. They instead look to have moved on with their pursuit of Raphael Varane.
There was also some reported interest from Arsenal, but that ended when it became apparent that Tomiyasu wanted to join Spurs.
The defender also had the option of staying in Italy and in Serie A with Atalanta, which would have given him the chance to play in the Champions League.
With this deal now being close, Spurs have also turned their attention to other areas that need addressing.
The club are now said to be considering a move for Porto midfielder Vitinha, who spent last season on loan at Wolverhampton Wanderers.
Vitinha’s agent, Jorge Mendes, has reportedly offered the 21-year-old to Spurs for a fee of around €20 million (£17 million).