The 44-year-old is expected to be confirmed as Garry Monk's replacement over the course of the next 24 hours.
The ambitious manager shocked the Elland Road faithful by resigning from the Championship club last month and has since taken over at the Riverside Stadium.
"We are delighted to make this announcement today as it successfully concludes what has been a thorough and extensive search, following a huge level of interest from all over the football world " Kinnear told the club's official website.
New Leeds owner Andrea Radrizzani is said to have met Christiansen last this week.
The Whites had been linked with Victor Sanchez, Alan Pardew, Quique Flores and most recently Fernando Hierro, but in the end the club has fooled us all by going left field with Christiansen, who didn't even feature in the betting until the very last second at 1/10!
Given the player's close bond with the manager and his previous words of praise for the new Boro boss, everything points to another blow for the Yorkshiremen if Bartley is given a choice between the Championship clubs.
As usual, Leeds United fans have taken to Twitter to react to the appointment.