The mail handlers, who work at post offices and mail-processing centers, sort mail, transport it within facilities and load and unload trucks.
The buyouts, to be pro-rated for part-time staff, will be available to almost all the USPS mail handlers except 2,000 who aren't career employees, CNN reported.
"The Postal Service is adjusting the size of its network to adapt to America's changing mailing trends," USPS spokesman Mark Saunders said in an e-mail.
The service seeks to reduce its workforce by 150,000 by 2015.
Saunders said he had "nothing to announce" on possible buyouts for other USPS employees.
The buyout resulted from negotiations between the USPS and the National Postal Mail Handlers Union.
The union said the buyout offer "is intended to provide a financial cushion, and added peace of mind, for mail handlers who might be prepared to move on to the next chapter of their lives."
For the first three months of this year, the Postal Service reported a $3.2 billion loss. It faces declining mail volume and a congressional mandate to pay in advance for retirement healthcare benefits.
Notable deaths of 2014 [PHOTOS]