Federer is set to play against Serbian Novak Djokovic, Austrian Dominic Thiem and Italian Matteo Berrettini.
The draw took place after the Nadal confirmed he would be travelling to London on Wednesday to prepare for the competition after he was given the all-clear following an abdominal strain, Efe news reports.
He is due to take to the courts on Sunday or Monday against Zverev for what will be the pair's sixth encounter. Nadal is the favourite to win.
Nadal has also won against Medvedev on the two occasions they have met, including the epic final this year at Flushing Meadows while Tsitsipas is the only competitor in the group who has had a taste of victory over the man from Mallorca.
The competition sets the path for the sprint to the top of the ATP rankings. If Djokovic sails through the competition unbeaten, Nadal must also make the final, the 640-point buffer he has over the Serbian allowing him just one slip up in London.
Each match won in the group stage in the ATP finals is worth 200 points, the semi-finals are 600 points and the final an extra 500.
Nadal is looking to win the competition for the first time. He has previously made two finals, the last one in 2013.
Federer has won the tournament six times, more than anyone else, while Djokovic has five to his name, level with Ivan Lendl.
( With inputs from IANS )