Councillors voted overwhelmingly in favour of the proposals at a meeting of the transport and environment committee this morning.
But they insisted the restrictions would not be brought in before 12.30pm, following a wave of opposition from religious groups.
Rev George Whyte, clerk to the Church of Scotland’s Edinburgh presbytery, previously told the Evening News churches would close if charges were introduced in the morning.
He said: “Our congregations see a bleak future for themselves if this goes ahead. Churches will close and what they do will be lost.”
Councillor Lesley Hinds, the city’s transport leader, said: “We will never satisfy everybody but I believe we have got a proposal here that is the right way forward.”
The new restrictions - which will not be introduced until 2018 at the earliest - will see parking charges brought in between 12.30pm and 6.30pm in the city centre.