Christiansen arrives at Elland Road having won the Cypriot top-flight with APOEL Nicosia last season, in a campaign which also saw him lead the club to the last-16 of the Europa League.
The Danish-born former Spain international's only other role in management saw him guide AEK Larnaca, another Cypriot club, to consecutive runners-up finishes.
Christiansen left APOEL last month after his 12-month contract with the club was not renewed following a defeat to Apollon Limassol in the Cypriot Cup final.
Speaking about the appointment, Angus Kinnear, Leeds United's managing director, said: “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.
“We wanted to appoint someone who can help us create a winning culture at the club and unite everyone connected with Leeds United, from the players to the supporters, ultimately taking the club back to where we all feel we belong.
We wanted to appoint someone who can help us create a winning culture at the club and unite everyone connected with Leeds United.
“Thomas was someone who had been on our radar from the very early stages of the process and quickly established himself as the outstanding candidate. We are confident we have found a man with who can work with us to take the club to the next level.”
Leeds began their search for a new manager three weeks ago after Monk, who guided the club to their highest league finish since 2011 last season, resigned from his position.
Monk's departure came less than 48 hours after Italian businessman Andrea Radrizzani had completed his takeover of the club from controversial owner Massimo Cellino.
Christiansen was not featured on the long list of candidates initially linked with the Elland Road job, with the likes of Jaap Stam, Aitor Karanka, Fernando Hierro, Alan Pardew and Victor Sanchez featuring among the bookmakers' favourites. However, it is understood that Christiansen was among Radrizzani's initial targets.
Christiansen, who won three senior caps for Spain as a player, will be unveiled at a press conference on Monday.
Additional reporting by PAReuse content