Warmbier's father, Fred Warmbier, told a news conference last week that his son had flourished while at the high school. Warmbier will be buried at Oak Hill Cemetery. Blue and white ribbons (the school's colors) adorned trees around the school to honor Warmbier.
The 22-year-old was medically evacuated to the United States last week with severe brain damage.
South Korea has said the North bore responsibility for Warmbier's fate and US President Donald Trump has slammed his detention and eventual death as "a total disgrace".
The exact cause of Warmbier's death is unclear. Hamilton County Cororner Dr. Lakshmi Sammarco said in a news release her office received and examined Warmbier's body but the family objected to an autopsy and the coroner only performed an external examination.
Among the speakers at the funeral were Warmbier's brother, Austin, his sister, Greta, and some of his friends, according to the funeral program.
After graduating as class salutatorian in 2013, Warmbier enrolled at the University of Virginia in Charlottesville, where he was studying at the school of commerce.
"He was able to connect with grownups and children, and he was one of those people that made you feel like you were his best friend, even though you had just met him", said his college counselor, Cynthia Meis, who attended the service.
His family had no news of him until 13 June, when Pyongyang said he had been in a coma since his trial after contracting botulism and receiving a sleeping pill.
"He was genuine and authentic, and so smart". The family does not believe that account.
A piece of legislation meant to curb American travel into North Korea got a boost in Congress on Thursday when House Foreign Affairs Chairman Ed Royce, a California Republican, agreed to move the bill through his committee. He was arrested just before departing Pyongyang International Airport.
A series of atomic tests and missile launches since past year have ratcheted up tensions on the Korean peninsula, and Warmbier's death has further strained relations between Pyongyang and Washington.
Warmbier, a 22-year-old University of Virginia student, died Monday, six days after he returned to his OH home in a coma after 17 months of detention in the North for taking down a political propaganda sign from a hotel.
Ohio Senator Rob Portman spoke before the funeral.
"We both agreed that our companies should not do business with any UN-designated North Korean entities in accordance with these resolutions", Tillerson told reporters following the meeting, adding that Washington sees North Koreas as a "top security threat".