Timberlake, 43, is expected to appear Friday in Sag Harbor Village court to plead guilty and pay a fine, resolving the misdemeanor charges, the sources said.
Timberlake was leaving the American Hotel when he was stopped for running a stop sign and swerving into the oncoming lane.
Video shows Justin Timberlake driving in Sag Harbor before arrest
The officer smelled booze on his breath, according to a police report. Timberlake told the officer he had had one martini and was following some friends home, according to police. He was arrested and spent the night in custody at a police station.
At a hearing last month, a judge suspended Timberlake's right to drive in New York.
His lawyer, Burke, has maintained that Timberlake was not drunk and that the case should be dropped.
Timberlake's license would remain suspended under the arrangement, although he is not a New York state driver.
Timberlake is believed to have to physically be in court to accept the plea.
(The Associated Press contributed to this report.)
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