Elorza said details of the agreement between bus company First Student and the Teamsters Local 251 were still being finalized and that members of the union must ratify it.
The strike began Sept. 27 and affects more than 9,000 schoolchildren. The dispute centered on retirement benefits.
"I am glad that both sides are heeding the call to put the needs of students and families first by engaging in constructive dialogue," City Council President David Salvatore said in a joint statement with Elorza.
First Student had released a statement earlier Friday calling on drivers to return to work Monday.
City officials had said they would consider requesting new proposals for school bus transportation.
Absences have risen as some students have had trouble getting to school, and the city hasn't provided any alternative transportation.
The American Civil Liberties Union of Rhode Island initiated legal action earlier this week against state educational officials for failing to provide transportation for students with disabilities, something the ACLU said schools are required under the law to provide.
A fire in the company's bus yard Thursday damaged more than half a dozen buses, First Student spokesman Frank McMahon said. Providence Public Safety Commissioner Steven Pare said while the cause of the fire remains under investigation, it is considered suspicious.
McMahon said he would not speculate on whether the fire was connected to the strike until the investigation is completed. The union condemned the property damage.
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