The Spanish club will compete in their second Club World Cup after finishing fourth in 2000, while Mexico's Cruz Azul are involved in thir maiden appearance, having already accounted for Western Sydney Wanderers 3-1 after extra time on Saturday.
That match was played in dreadful conditions with puddles forming on the pitch in Rabat as heavy rain fell throughout the contest, prompting Wanderers coach Tony Popovic to question why the game went ahead.
Following that rain, Tuesday's fixture has been moved from Rabat to Marrakech to give Real and Cruz Azul the best possible pitch to play on.
While Real are the clear favourites to win the Club World Cup - six of the past seven editions have been won by Europe's representatives - Cruz Azul coach Luis Fernando Tena insisted his team should not be discounted.
Real have never won the Club World Cup but did win the tournament's predecessor - the Intercontinental Cup - three times.
"Now we're looking forward to facing Real Madrid, who are probably the best team in the world right now," Tena said after his team's victory over Western Sydney.
"Of course, they're the favourites but there are always surprises in football."
Real will enter the match on a 20-game winning streak in all competitions, while Carlo Ancelotti's men lead La Liga by four points from archrivals Barcelona, following their 4-1 win at Almeria on Friday.
Cruz Azul had only won one of their previous six matches before downing Western Sydney in Morocco, with Tena's side needing some luck to get past the A-League outfit.
The Wanderers took the lead in the 65th minute through Iacopo La Rocca but, after Matthew Spiranovic was sent off nine minutes later, a late penalty allowed Gerardo Torrado to equalise for Cruz Azul.
Western Sydney also lost captain Nikolai Topor-Stanley to a second yellow card in the 102nd minute and Cruz Azul pounced, with Mariano Pavone scoring six minutes later before Torrado converted another spot-kick in the 118th minute to complete the victory for the Liga MX club.
