The large 10ft-high black-painted boards sparked complaints that famous views of the Castle were being blocked during the peak tourist season.
Benches along Princes Street also had barriers put in front of them to prevent anyone standing on them to look over the railings.
As annoyed residents took to social media to complain about the moves, council leader Adam McVey intervened, tweeting that he had asked officials to remove the barriers as soon as possible and saying he wanted a guarantee they would not be erected for any future events.
He added: “This is public space and these are public views. Ticketed events cannot put up barriers which are to the detriment of the city.”
The council said the screens - which went up ahead of last Monday’s concert by Tom Jones - were agreed with organisers in May as part of the safety provisions for the event to prevent people climbing over the railings into Princes Street Gardens or crowds spilling into the road.
But hastily-called meetings yesterday led to the boards being removed in preparation for Rag ‘N Bone Man performing at the bandstand on Tuesday. Paloma Faith, Kasabian and Brian Wilson from the Beach Boys are due to hold concerts there on Friday, Saturday and Sunday.
Instead, the pavement on the Gardens side of Princes Street in front of the bandstand will be closed during the concerts.
At least one bus stop will have to close temporarily during performances. Talks are understood to be continuing with Lothian Buses.
Before the arrangement was announced Cllr McVey tweeted again, saying he had met council chief executive Andrew Kerr and deputy council leader Cammy Day on the issue. “Alternative options to ensure public safety during concerts being explored with organisers. Confident public views will be restored but this won’t mean folk get a ‘free’ view of the stage, nice try though!”
Later, Cllr McVey said: “I’m really pleased to see a less imposing solution found, one which will – crucially – provide the same level of public protection but allow the view of the Gardens and Castle to remain undisturbed. This is a public park and the removal of the barriers helps us to strike a better balance.”
The council said screens had occasionally been in place on this part of Princes Street in previous years for events at the Ross bandstand.
And it said the pavement along Princes Street had also been cordoned off previously to prevent people from gathering and spilling out on to the road and to stop people from climbing the fence.
This year it had been agreed, at the request of Lothian Buses, to keep the pavement and bus stop open, but to erect the screens.
They had now been removed because they were obstructing views.
The council said the necessary pavement area would be cordoned off during concert hours only.