The first leg which was supposed to be played in Germany also took place at the Puskas Arena on February 16 after the away side were barred from entering the home side’s country due to coronavirus restrictions.
Leipzig 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, Liverpool won the first leg 2-0, with goals from Mohamed Salah and Sadio Mane putting Jurgen Klopp’s men within touching distance of the quarterfinals.
The European football authority said in a statement on Thursday morning: "UEFA is able to officially confirm that the Champions League round of 16 second leg match between Liverpool and RB Leipzig will now be played at the Puskas Arena in Budapest. The date of the match (March 10, 2021) and the kick-off time (9pm CET) will remain the same.
"UEFA would like to express its gratitude to Liverpool and RB Leipzig for their support and close cooperation, as well as the Hungarian Football Federation for their assistance and agreeing to stage the match."