Bomb disposal officers detonated the item after it was found in the mailroom on Wednesday morning.
Police Scotland is now “working closely together” with officers investigating finds at Heathrow and London City airports and Waterloo station.
Staff and students were evacuated from buildings and no-one was injured.
Classes were expected to return to normal on Thursday
Assistant Chief Constable Steve Johnson of Police Scotland said: “The package sent to the university was not opened and no-one was injured. A controlled explosion of the device was carried out this afternoon by EOD.
“There are similarities in the package, its markings and the type of device that was recovered in Glasgow to those in London.
“Therefore, we are now treating it as being linked to the three packages being investigated by the Met in London and both investigations are being run in tandem.
“Our inquiries into the Glasgow package are at an early stage but there is no ongoing risk to the public.”
He added: “Anyone who sees something suspicious should report it to the police immediately.”