The Denmark international was at the club’s Hotspur Way training ground on Monday to undergo a medical for the deal.
Now according to Talksport, Tottenham have now completed the deal which will see Hojbjerg become Jose Mourinho’s first signing of the summer.
The 25-year-old is understood to be joining Spurs for an initial £15m which could rise to more than £20m with add-ons.
It is also been previously reported that right-back Kyle Walker-Peters is set to go the other way in a separate deal.
Hojbjerg arrived in England in 2016 from Bayern Munich, where he also worked under Pep Guardiola and impressed at St Mary’s, soon taking on the armband.
He was recently stripped of the captaincy after he informed the south coast club that he would not be signing a new deal and spent much of the resumption of the 2019-20 campaign out of the side.
There was interest from Everton, but the midfielder was keen to work with Jose Mourinho at Spurs, who look to have got the deal done in an uncharacteristically swift manner.