Tottenham Spurs have agreed a deal of £15m plus bonuses to sign the Denmark midfielder from the Saints.
Kyle Walker-Peters is expected to move the opposite way for an initial £12m – but personal terms between are yet to be agreed.
Sky Sports News exclusively reported in January that Hojbjerg was a target for Jose Mourinho as he looks to mould the squad in his image.
Both Spurs and Everton opened talks with the south-coast club last month but it soon became clear Hojbjerg was keen on the move to north London over Merseyside.
He is now set to have his medical at Tottenham’s facility on Monday.