Chesterfield County Sheriff's Department members participating in the search made the discovery before noon in southern Albemarle County in central Virginia, according to Charlottesville Police Chief Timothy Longo.
Shortly thereafter, a detective relayed the news to Graham's parents.
"These are human remains and forensic tests need to be conducted to determine the identification ... " Longo told reporters. "But nonetheless we wanted to be quick and timely to share that information with the Graham family."
The discovery comes 35 days after Graham was last spotted, on several surveillance cameras, in Charlottesville's Downtown Mall area. That footage showed her leaving the Tempo Bar at around 2 a.m. on September 13, as well as a man -- later identified by authorities as Jesse Matthew, 32 -- following her.
On September 24, Matthew was taken into custody while camping on a beach in Galveston, Texas, some 1,300 miles from Charlottesville. He is the only person detained in connection with Graham's disappearance, charged with abduction with the intent to defile.
He has also been linked by forensic evidence to the case of Morgan Harrington
, a 20-year-old Virginia Tech student who was last seen hitchhiking along U.S. 29 outside of Charlottesville in October 2009. She was found dead on a nearby farm the following January.
No arrests have been made in Harrington's case, and the cause of her death still is under investigation. Police, though, did recently seize a cab owned by Matthew that he was driving in Charlottesville in 2009, a source with knowledge of the investigation told CNN.
Matthew's next court appearance in relation to Graham's disappearance is scheduled for December 4.
Officials didn't say whether charges against anyone were imminent in light of Saturday's discovery.
'A great deal of work ahead'
Albemarle County Police Chief Steve Sellers did appeal to anyone who was in or knows the area in which the remains were found to contact authorities if they saw "any suspicious activity" or "an individual fitting Jesse Matthew's description in that area about that time."
"Today's discovery is a significant development, and we have a great deal of work ahead of us," said Sellers, noting Graham's case is now considered a "death investigation." "We cannot and we will not jump to any conclusions."
The 18-year-old Graham was in her second year at the University of Virginia -- a member of the ski team and making straight A's, her parents say -- when she was last seen.
"She was extremely smart, very witty, very athletic," said Craig Maniglia, the coach of the high school softball team that Graham co-captained in Northern Virginia.
Graham's last contact with friends -- telling them she was lost and trying to find a party, according to CNN affiliate WVIR -- came via text message at 1:20 a.m. the morning of September 13.
Her disappearance prompted a massive search involving more than 1,200 volunteers, not to mention emotional appeals from officials like Longo and Graham's parents.
Sunday's scheduled public search of Walnut Creek Park -- not far from where the remains were found -- was canceled, the Virginia Department of Emergency Management said in a statement.
"Authorities are focusing their attention on recent evidence, which limits law enforcement resources necessary to carry out a public search," the agency said.
Social media commenters saddened
Earlier this week, John and Sue Graham pleaded for help finding their daughter, saying, "It is heartbreaking for us that the person or persons who know where Hannah is have not come forward with that information. It is within their power ... to end this nightmare for us all."
Her friends hadn't relented, either.
In a statement released to CNN, they asked 'that everyone in Charlottesville and surrounding areas be on the lookout for new clues. No clue is too small and every search of personal property, even if it does not yield a result, is helpful."
Their efforts continued as recently as Saturday, with the "Help Find Hannah Graham" Facebook page
posting pictures of various volunteers handing out ribbons to businesses in downtown Charlottesville.
Later in the day, that page was full of heartfelt reactions from friends and strangers alike. One woman wrote, "Rest in peace beautiful angel."
And a man chimed in, about hearing the news: "I wept as if she were family."
Coy Barefoot, a member of the University of Virginia adjunct faculty and a local media personality, told CNN that Saturday's discovery -- and the prospect it could contribute to breakthroughs in the cases of other missing women, such as Harrington -- stirred "a mix of emotions here in Charlottesville."
"I have seen people crying. I have cried tears myself," said Barefoot. "But you're also, in the same moment, so relieved that there might be some closure for such a wounded family for such a wounded community."