Authorities say their father, Lee Giordano, 28, contacted police on Monday to say the kids are with him and are fine.
Brianna Giordano, 5, and Lee Giordano Jr., 2, were last seen going out for ice cream with their father on Sunday afternoon.
The three hadn't been heard from by lunchtime on Monday, when the prosecutor's office issued an alert.
In a news release on Monday evening, the prosecutor's office said Giordano and his wife are not divorced and have no custody arrangements ordered by court, so "as the children's father he does not have a legal obligation to notify his wife if he chooses to travel with his children. No laws have been broken."
They say he has also contacted his wife and let her know where he and the children are.
The prosecutor's office also said Giordano told them he is working to resolve a custody issue in Florida, where the couple lived recently.
The prosecutor's office said it is "not pursuing involvement in the case."