Green was born in the Netherlands around 1720 emigrated to America in her youth. On April 25, 1738, she married Jonas Green, a son of New England printers, in Philadelphia. Shortly after their marriage, the Greens moved to Annapolis, where Jonas set up a small print shop in a house on Charles Street.

Between 1738 and 1760, Green gave birth to fourteen children, eight of whom died young. Green spent her time with domestic responsibilities, as well as advertizing the sale of goods like coffee and chocolate in her husband's newspaper, the Maryland Gazette.

Jonas Green died in 1767, leaving Anne Catharine Green with debt, a print shop, and six children to take care of. Green decided to take over Jonas' print shop and continued uninterrupted publication of the only newspaper in Annapolis at the time. Green fulfilled her husband's contract with the government, publishing the Acts, Votes, and Proceedings of the Maryland Assembly on time. Her reliability earned her the same contract the next year, but in her own name.

Green moved her print shop supplies into the family home to help her manage her tasks as a single mother and business owner. Her son, William, began helping with his mother's business in January 1768, however she had to resume solo publication of the Maryland Gazette following his death in 1770. Green's son, Frederick, later helped with publication of the paper.

As a colonial printer, Green covered the issue of independence as well as local controversies. She published the famous �ntilon/First Citizen debate between Daniel Dulany and Charles Carroll of Carrollton, in which Carroll argued for an independent legislature and the privileges of citizenship. Her publication of Elie Vallette's Deputy Commissary's Guide, prepared by silversmith Thomas Sparrow, contains the only engraved title page from a colonial Maryland press.

Green proved to be a successful businesswoman; she paid off her late husband's debt in less than three years after his passing. Her competence in handling money also allowed her to buy the building that housed her family and the print shop, which had been leased while Green's husband ran the business. Her confidence shone in her decision to commission a portrait of herself by one of the foremost colonial painters, Charles Willson Peale. She posed with a paper in the lap that reads, "ANNAPOLIS Printer to�" displaying Green's confidence in a role that broke tradition at the time.

Anne Catharine Green died on March 30, 1775, survived by five of her children. Her accomplishments as a printer, publisher, and a single mother encouraged the position and abilities of women in a time when they were expected to remain in a domestic role.