The large number of supporters due to attend the game at Murrayfield is expected to place huge pressure on the new system and the city's bus and train operators.
Edinburgh Trams are putting on an enhanced service before and after the game, which kicks off at 7.45pm, and extra buses and trains are also running.
ScotRail will be providing extra carriages on the Glasgow to Edinburgh line via Falkrik which will run quarter-hourly most of the day.
The return leg of the UEFA Champions League qualifier is being played at the Edinburgh stadium rather than at Hampden, as the Glasgow ground is a venue for the Commonwealth Games.
Currently the tram system takes around 90,000 passengers a week, but the number is expected to soar this week as many of the 40,000 fans attending the game will want to travel by tram - which stops right outside Murrayfield.
A new Desso hybrid pitch has just been completed after four months intensive work and the new pitch has also been moved nearer the west stand.
Dominic McKay, Scottish Rugby's director of commercial operations, communications and public affairs, said: "The BT Murrayfield pitch is in excellent condition and we're hugely proud of what has been achieved, in a relatively short space of time, to ensure we have a playing surface our supporters will be proud of.
"We look forward to welcoming Celtic, KR Reykjavik and their supporters to BT Murrayfield and wish them the best of luck in this important European qualifier."
Last month extra tram workers were on duty to guide people and help them use the service as 50,000 music fans headed for the One Direction concert at Murrayfield.