The Whites reached an agreement over a fee with Salzburg earlier this week and have been confident of wrapping up the deal soon.
Kristensen has been on national duty with Denmark but flew to England to undergo a medical at Leeds today.
The Whites put him through his paces and the defender has successfully completed the medical with the Whites.
Leeds are now looking to sort out the paperwork to wrap up the deal and seal their second signing of the summer.
The Dane will sign the contract with Leeds and he is expected to seal the move by the end of the day.
Leeds have been in the market for a right-back this summer due to serious injuries to Luke Ayling and Stuart Dallas.
Kristensen was identified as their top target and an impressive pitch from Leeds helped them to beat Borussia Dortmund to his signature.
Jesse Marsch is keen to complete the bulk of the transfer business early after Leeds narrowly avoided relegation last season.
