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Plans to lay off 4,100 teachers were averted late Friday evening as part of a deal struck between the Bloomberg administration, the City Council and the teachers unions.

At least two union concessions and restoration money from the City Council were negotiated into the deal in order to save the jobs.

The first concession is that all one-year teaching sabbaticals are suspended for the 2012-2013 school year. The sabbaticals allow teachers to remain partially-paid while they take an extended leave of absence. The agreement will not apply to the health restorations.

A city aide confirmed the deal and estimated that the suspended sabbaticals would save the city $17 million.

The second concession is that teachers in the Absent Teacher Reserve, or ATR, will be redeployed to fill substitute teaching positions, which are currently filled by teachers who work on a per diem basis. The daily rate for substitutes is approximately $154.97  (and $180/day for subs who have filled in for longer than 30 days). That money would be saved because the ATR, a pool of teachers without full time positions who remain on payroll, would be able to replace those spots. Under the agreement, each week teachers from ATRs can be sent to a different school in their district.

Put together, the concessions are expected to save the city a total of $60 million.

“I want to thank all the parties involved in this agreement for their willingness to come together to prevent the harm that would come to our students from a massive loss of public school teachers,” UFT President Michael Mulgrew said in a statement. “In particular I’d like to cite the key role played by Council Speaker Christine Quinn and her members and staff, along with Chancellor Dennis Walcott and the DOE officials who worked with us to find ways to prevent what could have been a disaster for our schools.”

The budget deal also found money to keep open 20 firehouses that were slated to close under Bloomberg’s budget. More than 1,000 jobs in non-uniform and non-pedagogical titles could not be saved from the deal, however.

It’s not immediately clear how long the agreement would last, or whether it requires approval from then entire union membership. A press conference with UFT President Michael Mulgrew is scheduled in downtown Manhattan at 10:30 p.m. tonight.

Chancellor Walcott emailed principals later Friday night to inform them of the budget agreement and said to expect their budgets by Monday afternoon. He alluded to the anticipated cuts, which he called “difficult, but necessary, decisions.”

“Each school will face difficult choices, but I am confident that you are the best group of principals in the history of New York City’s public schools and will meet these challenges head on,” Walcott wrote in the email. He did not specify the percent of the cuts.

The City Council still needs to vote on the final budget, which it has until Thursday, when the 2011 fiscal year ends.