A post on the Utility Workers Union of America Local 1-2's Facebook page said a tentative agreement is in place.
More than 8,000 utility workers had threatened to walk off the job starting at midnight on Sunday.
Details of the agreement have not been released.
The union said Saturday that a long, hot summer would put major strain on the electrical grid and, with no deal in place, would be a disaster waiting to happen.
Local 1-2 President James Shillitto said Con Ed paid no heed to the sacrifices by the more than 700 members sickened by COVID-19.
Shillitto said his Local 1-2 workers are first-responders in any emergency and vital to any recovery effort.
Con Ed has not responded publicly.