The Good Morning Britain presenter insisted the award should have been given to healthcare workers on the coronavirus frontline. Mr Morgan tweeted: “Wrong call. They haven’t done anything yet. You should have given it to the frontline health care workers.”
Many of the former newspaper editor’s Twitter followers were quick to agree with him.
One commented: “Agree health workers all the way 2020….”
Another wrote: “I completely agree.”
A third said: “Exactly, or the couple who designed the vaccine.”
The magazine’s editor-in-chief Edward Felsenthal said: “For changing the American story, for showing that the forces of empathy are greater than the furies of division, for sharing a vision of healing in a grieving world, Joe Biden and Kamala Harris are TIME’s 2020 Person of the Year.”
Mr Biden and Ms Harris are yet to comment on the accolade.
Time has been naming its Person of the Year since 1927.
The Person of the Year is usually an individual, but groups have previously been chosen.
The winner is deemed to have “affected the news or our lives the most, for better or worse”.
Mr Trump was Time’s Person of the Year in 2016.
Last year, the award was won by teenage environmental activist Greta Thunberg.