Dozens of police cars took part in a funeral procession from Lumberton Senior High School - where Goodson was a school resource officer - to the nearby Gardens of Faith Cemetery.
Police officers from as far away as Tennessee and New York were in Lumberton to honor Goodson.
Fire trucks were parked along the route and Lumberton residents stood on sidewalks to watch the hearse pass by.
Goodson's flag-draped coffin was transferred to a horse-drawn caisson for the last part of the trip.
Among those in attendance at the funeral was Raleigh Police Chief Harry Dolan, who is a veteran of the Lumberton Police Department.
"This is heartbreaking for all police officers all through the country, and for us in the Capital City police department to be here and recognize the family and to have personally have served as a Lumberton police officer for six years similarly to Jeremiah," said Dolan. "It was very important that I be here."
Goodson's widow, Lametria, is expected to give birth soon to the couple's third child, a boy.
The 32-year-old Lumberton police officer was shot and killed last week while trying to serve a warrant. Marques Brown, 27, is now charged with first-degree murder.