The first leg which was supposed to be played in Germany also took place at the Puskas Arena on February 24 after the away side were barred from entering the home side’s country due to coronavirus restrictions.
Monchengladbach were due to travel to England next week to fulfill the second leg but were informed by the German government that they would need to undergo a period of isolation if they returned home.
As the away side, City won the first leg 2-0, with goals from Bernardo Silva and Gabriel Jesus putting Pep Guardiola’s men within touching distance of the quarterfinals.
"UEFA is able to officially confirm that the UEFA Champions League round of 16 second leg match between Manchester City and Borussia Monchengladbach will now be played at the Puskas Arena in Budapest," read a statement from UEFA on Wednesday.
"The date of the match (March 16, 2021) and the kick-off time (21:00CET) will remain the same.
"UEFA would like to thank Manchester City and Borussia Monchengladbach for their support and close cooperation, as well as the Hungarian Football Federation for its assistance and agreeing to stage the match."
City added: "Changes to the German COVID-19 regulations mean that the visitors are unable to travel to the UK to play the return leg in Manchester as originally planned."