Traffic began flowing in the central Cairo thoroughfare by early Tuesday evening.
Earlier, hundreds of soldiers took positions in the middle of the square, and military vehicles were seen at every entrance to the normally busy thoroughfare.
Protesters had earlier closed the square to traffic by setting up barricades.
Troops with machine-guns detained several young men, pushing them into police vans, while others broke down the barricades and rolled up coils of barbed wire.
Men were also seen picking up debris from across the square, which had been the focus of an 18-day popular uprising against Mubarak, who was forced to resign from office on February 11.
Dispute over operation
A youth coalition that had been involved in the uprising said that it had persuaded the remaining protesters to reopen the square because they were causing more harm than good by staying.
"We met with the [ruling] military council yesterday and discussed opening Tahrir. We agreed to end the protest and give the army a chance to proceed," said Mohamed Sukri, a member of the Revolutionary Youth Coalition.
"The military council thanks the youth of the January revolution for returning Tahrir Square to normal," it said in a statement.
Mohamed Zaidan, a protester who was at the square when the army arrived, however, gave a different account.
"We didn''t agree with anyone to clear Tahrir," said the 25-year-old Zaidan.
"We were attacked by rock-throwing people who wanted to force us out and then the army came, didn''t speak to us and suddenly moved in to force us out of the square."
An earlier attempt by the army to clear the square resulted in at least one death and injuries to 71, after they were accused by protesters of using live ammunition.
Some Cairo residents have voiced concern and exasperation at the continuing Tahrir protests, which have occupied the square since a Friday demonstration that was attended by hundreds of thousands.
The demonstrators were demanding that the head of the military council, Field Marshal Hussein Tantawi, the Mubarak-appointed defence minister, step down, and that Mubarak stand trial for corruption.
Mubarak was taken to a hospital on Tuesday after suffering heart problems while being questioned by authorities regarding the corruption allegations.