The game was meant to be played at Myreside but freezing temperatures have caused the change of venue.
Murrayfield has undersoil heating, unlike Watsonians’ ground.
A statement from Edinburgh said: “Inspections of the Myreside surface, which has had protection in place all week, were carried out on Friday evening and Saturday morning.
“In consultation with the match officials and owing to freezing temperatures, with a further drop expected later today, it was decided the game should be moved to guarantee it goes ahead as planned. The club also felt it important that making an early decision would help assist supporters in adjusting their travel plans accordingly.
“Undersoil heating has been on at BT Murrayfield as part of the club’s contingency plan, and we are fortunate to have such a great a facility to ensure the match goes ahead this evening.”
All existing match tickets are valid and tickets will be available to buy online up until kick-off at edinburghrugby.org.
Edinburgh are top of Pool 4 in the Challenge Cup after away wins over London Irish and Russian side Krasny Yar.
Meanwhile, the BT Premiership match between Currie Chieftains and Boroughmuir at Malleny Park has been postponed.