Workers discovered human remains while installing a lift at a council office.
The men came across the bones on Wednesday as they worked at Blaby District Council's offices in Desford Road, Narborough.
Police officers and a forensic team were called and the area was cordoned off for most of the day.
Analysis confirmed the bones are at least 70 years old. Police said there were no suspicious circumstances.
A spokeswoman for the council said part of the building was situated over a former rectory, which could explain the find.
However, Tom Seaton and Adam Bride, who found the remains, said it was still quite a shock.
Tom, 20, from Cleethorpes, said: "We started digging the hole and we found bones. We kept digging and found more.
"The first thing we found was part of a leg and we then found fingers, ribs, a skull, a pelvis, arms and legs.
"We thought it was a human, definitely.
"We probably found about half a bin bag full of bones."
The pair discovered the bones at 8am on Wednesday.
"The police sent some forensics staff who said they were definitely human bones, but they were too old to be anything untoward," said Tom.
"I thought it was quite exciting."
Adam, 44, also from Cleethorpes, said finding bones was fairly common when digging. "However, as we went a bit further we realised the bones were definitely human," he said.
"You could see that by the size of them. Then we dug up a skull."
The bones are being stored in the council building until they can be buried at a church.
A spokeswoman for the council said a hospital professor attended the scene along with the forensic officers.
She said: "Due to the condition of the bones and the building's location in relation to the nearby church and graveyard, the case isn't being treated as suspicious.
"There were no marks on the bones to suspect foul play and forensics have been unable to date them other than they are at least 70 years plus.
"Because they can't date them, as they're in fragments and without any teeth, they are not able to go any further.
"They are currently being stored here, but the church is being contacted."
She said as the builders were not digging any deeper, they were unlikely to come across any other human remains.
A police spokesman said: "We were called at 9.16am on Wednesday after pieces of bone were found during building work at a premises in Desford Road, in Narborough.
"Scenes of crime officers attended.
"There were no suspicious circumstances and the coroner has been informed."
