The Reds recently temporarily closed their first-team training centre after assistant manager Pep Lijnders became the latest to have to isolate, moving the first leg at Anfield to 13 January and the second at Emirates Stadium on 20 January, both at 19:45.
Liverpool had requested the postponement.
The EFL said in a statement that it had been in “regular dialogue” with the club since then “in an attempt to understand whether the tie could proceed”.
The statement read, “Significant developments over this period have resulted in the club reporting an ever-increasing number of Covid cases.
“Having now fully reviewed the circumstances involved, the League has accepted Liverpool’s request after determining, albeit reluctantly, that a postponement was the only option as the club looks to mitigate against the further risk of infection amongst its squad and staff alongside ensuring public health was protected by not travelling from Liverpool to London”.