The Danish midfielder is set to have a medical after the weekend to complete the deal, in what would be Jose Mourinho's first major signing at the club.
The Spurs boss sees Hojbjerg as a key pivot in his team, after impressing at Southampton.
Kyle Walker-Peters is set to go the other way for £12m. Hojbjerg would become one of a select band of players to play for both Mourinho and Pep Guardiola.
Hojbjerg was stripped of the Southampton captaincy before the end of the Premier League season by manager Ralph Hasenhuttl after informing the club of his desire to leave, having arrived from Bayern Munich back in 2016.
The Dane took on the captain’s armband in December 2018 following Hasenhuttl’s appointment, but his public declaration that he wanted to seek a summer transfer saw James Ward-Prowse replace him during the delayed season run-in.