Carlo Ancelotti's side will be intent on securing a first-leg advantage ahead of their short trip to the Estadio Vicente Calderon when they host Los Rojiblancos
The rivals met five times in all competitions last term, including the European showdown in Lisbon, which Los Blancos won 4-1 after extra time.
Carlo Ancelotti's side also came out on top when the clubs clashed in the Copa del Rey - running out 5-0 aggregate winners in the semi-finals before beating Barcelona in the final - but Atletico had the edge in La Liga, taking four points off Real on their way to winning the title.
The European champions picked up where they left off last season by seeing off Sevilla in the Super Cup last week and Atleti have also got their hands on some pre-season silverware already by winning the Ramon de Carranza Trophy.
While Madrid's win in Cardiff represents a bigger achievement than Atletico's close-season successes against the likes of Wolfsburg, Cadiz and Sampdoria, midfielder Mario Suarez feels that his team-mates can build on last season's momentum - starting in Tuesday's first leg at the Santiago Bernabeu.
"We play every game like it's our last. Every game is important. The team played well and we felt good [against Sampdoria]," said the Atleti star.
"On Tuesday we have to play for an important title against our long-time rival and we'll face it as we always do. We'll go to win and everyone knows it. It will be very difficult."
Victory in the Supercopa would represent an ideal boost for both sides ahead of their Primera Division openers later in August - with Real and Atletico taking on Cordoba and Rayo Vallecano in their respective curtain-raisers.
Real ended their close-season friendlies with defeat to Fiorentina on Saturday - with their only win since lifting the Champions League coming against Sevilla in the Welsh capital last week.
Despite struggling for victories in recent weeks, big-name arrivals such as James Rodriguez and Toni Kroos have both got playing time under their belts alongside the likes of Cristiano Ronaldo and Gareth Bale.
Ancelotti's main selection dilemma for the visit of Atleti will likely come in goal, with recent signing Keylor Navas and long-serving captain Iker Casillas vying for the No.1 spot.
"We'll make the decision on who plays in the Supercopa later on," said Ancelotti prior to the Fiorentina game, in which Navas made his Madrid debut.
The Italian may call on Bale (back) and Pepe (calf) for Tuesday's clash after they failed to feature in Saturday's loss while Ronaldo - who scored twice against Sevilla - also looks to have shaken off injury worries that dogged him at times last season and during the World Cup.
"[Ronaldo] is ready for the Supercopa without any issues," Ancelotti confirmed.