"The camp will be packed up as soon as our council trucks can help them with that.
"They realised pressure was mounting and the crisis was developing," she said.
The agreement comes after the ever fractious relationship between the city council and NSW Government deteriorated even further due to the camp. There was even mutterings of sacking the council.
"The talk about clearing out Martin Place and throwing people into the back of trucks was really scary for those vulnerable homeless people in Martin Place and that's not what we are about as Sydney citizens," Moore said.
Council will put up $100,000 towards a safe space with the NSW Government putting in another $100,000 for a facility, most likely in the inner city suburb of Redfern, for homeless people. This would include a kitchen and support services.
But Ms Moore could not guarantee the camp wouldn't return despite the agreement, with some saying it could now crop up in Hyde Park.
"We all know until we have some long term solutions to the housing crisis in our city we'll see another tent city in the not too distant future," Moore said.
She said the new facility was "not a sleeping place, it's a communal place".
Priestly said he was "surprised" at suggestions the new safe space wouldn't include accommodation. That was key, he said, to people moving on.
"Quite clearly a safe space includes somewhere for people to sleep. It's absurd to provide a safe space when people are awake and not when they're asleep.
"I don't want to be there any longer than absolutely necessary if we work on something sustainable. But if we cobble something together it will fall apart and you will have the same problem."
Taking to news.com.au, Priestly said he was "optimistic" the deal would work but the camp would only be cleared when there was a "safe" place for people to sleep.
While Family and Community Services had offered accommodation to those at the camp, Priestly said some offers were either in unsafe residences or not suitable. In one situation, he said, a person in a wheelchair had be given accommodation several stories up in a building with no lift.
After hearing of the deal, City of Sydney Labor councillor Linda Scott said: "While I welcome Clover Moore supporting $100,000 for a safe space for those sleeping rough in Martin Place, it's disappointing it took the threat of putting the City into administration to see it happen."
The more than 40 tents, which have been dismantled by the authorities once already, stretch across the pedestrianised plaza outside the Reserve Bank headquarters in Sydney's CBD and have become the centre of a slanging match between the NSW Government and City of Sydney.
Earlier the NSW Premier Gladys Berejiklian issued a final ultimatum to the council warning them to remove the homeless settlement, or the state government would.
On Tuesday, Premier Berejiklian said housing staff has visited the camp 41 times to offer alternatives to sleeping rough, but some had no intention of moving.
Sydney Lord Mayor Clover Moore previously said she wouldn't support moving the homeless "without certainty they have support and permanent homes to go to."
"That isn't politicking, it is doing my job to support society's most vulnerable, as my community expects," Moore said in a statement on Sunday.
Berejiklian said Family and Community Services staff had been to the camp 44 times and found 70 people accommodation.
"Anybody who wants to be elsewhere will be provided that accommodation," she said.
Opposition social housing spokeswoman Tania Mihailuk called on the state government to end the stand-off and do more to tackle homelessness in NSW. Mihailuk said a lack of social and affordable housing was contributing to the problem.
"The current housing crisis has led to a situation where the only option for many people is crisis accommodation, couch surfing or rough sleeping on the streets," she said.
