Cheers erupted just after 1 a.m. Friday when Police Superintendent William Evans announced police had no plans to raid the square, The Boston Globe reported.
Boston Mayor Thomas Menino had warned protesters Thursday morning that further action would be taken if they didn't leave by midnight.
Anticipating a police raid, some protesters packed up belongings and headed home. The newspaper said food, tents and valuables were removed from the square and sleeping arrangements were made for "vulnerable" members of the encampment.
Police said they hope remaining demonstrators will leave the camp voluntarily.
In Los Angeles, Arthur Rodriguez, 27, the grandson of labor and civil rights leader Cesar Chavez was reported to have been among scores of people arrested last week when police closed an Occupy LA encampment at City Hall.
His father, Arturo S. Rodriguez, who was married to the late Linda Chavez Rodriguez and is president of the United Farm Workers, announced his son's arrest in a statement on the union's Web site.
"We are proud of Arthur for his activism and commitment in the tradition of his grandfather, Cesar Chavez, and the farm worker movement," his father said. "We are proud he and his fellow occupiers maintained their discipline of non-violence both during their arrests and while at the detention center."