Dragusin has been given the green light to fly to London to undergo his medical later on Wednesday.
Spurs currently have just two fit centre-backs in their ranks and have moved quickly to use the January transfer window to reinforce their defence.
Ange Postecoglou's side were able to agree a package with the Italian club worth £25million plus add-ons and Djed Spence going on loan.
Bayern made a late bid to hijack the deal for the Romania international.
Dragusin was promoted from the Juventus academy into the first-team and was sent on loan to Sampdoria and Salernitana.
READ MORE ON TRANSFERS
Henderson linked to Newcastle and Ajax, but Al Ettifaq will not be pressured into selling
Ivan Toney hints at Brentford future amid Arsenal and Chelsea links
He first joined Genoa when they were in Serie B last season on a loan deal, which became permanent after several objectives were met.
The centre-back has made 22 appearances this season and scored two goals, with a move away already being touted.
With Bayern missing out on Dragusin, they are likely to step up their pursuit of Eric Dier, who is seemingly not part of Postecoglou's plans at Spurs.
The German giants reached a verbal agreement with the defender over a potential move this month.
Dragusin will be Tottenham's second signing of January with Timo Werner completing a loan deal until the end of the season from RB Leipzig.
Micky Van de Ven talks about his return from injury to the Tottenham squad