Nancy took charge on December 3, but his month-plus at the Scottish giants has been anything but successful.
His team has lost six of eight matches - including the League Cup final against St Mirren - and the latest setback, a 1-3 loss to arch-rivals Rangers in the "Old Firm", was the last straw.
"Celtic today announces that we have decided to terminate the contract of Wilfried Nancy with immediate effect," the club said in a statement.
Wilfried Nancy signed in December on a 2.5-year deal after leaving American side Columbus Crew.
In addition to Nancy, his three assistant coaches and sporting director Paul Tisdale will also be leaving their positions, according to Celtic's website.
Martin O'Neill, 73, will take over as manager until the end of the season. He managed Celtic from 2000 to 2005 and for eight games earlier this season following the departure of Brendan Rodgers at the end of October.
