The 23-year-old underwent the final part of his medical on Thursday and assuming no complications, he is then expected to fly to London to finalise the paperwork.
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Spurs have agreed a deal believed to worth €50m with €5m in add-ons in a transfer that will rank as the second most expensive in the club's history after Tanguy Ndombele's €60m ($71m) arrival from Lyon in July 2019.
It would also be the third signing of new head coach Nuno Espirito Santo's tenure after goalkeeper Pierluigi Gollini arrived on loan also from Atalanta and Bryan Gil joined the club from Sevilla in a move which saw Erik Lamela travel in the opposite direction.
Spurs' pursuit of Romero is believed to have been influenced by the club's managing director of football, Fabio Paratici. The centre-back was named Serie A's Defender of the Year last year during a campaign in which he made 42 appearances across all competitions as Atalanta finished third and lost the Coppa Italia final to Juventus.
Romero joined Atalanta on a two-year loan from Juventus at the start of the 2020-21 season with the option to make the deal permanent for €16m ($19m), payable in three instalments.
Spurs were keen on signing a centre-back throughout last season and with former boss Jose Mourinho identifying Inter Milan defender Milan Skriniar as his preferred target. However, the clubs could not agree a fee and the arrivals of Nuno and Paratici have seen Tottenham shift their focus elsewhere.