Parcel bombs sent to Celtic manager Neil Lennon and two high-profile fans of the club were designed to cause "real harm", according to police.
The liquid-based devices were addressed to Lennon, Paul McBride QC and former Labour MSP Trish Godman.
Strathclyde Police Det Supt John Mitchell, of Strathclyde Police, told a press conference it had been a "despicable and cowardly act".
The devices were found at various locations in the west of Scotland.
The first suspect package was intercepted by the Royal Mail in Kirkintilloch, East Dunbartonshire, on 26 March and was addressed to Mr Lennon at Celtic's training ground in nearby Lennoxtown.
Two days later a device was delivered to Labour politician Ms Godman's constituency office in Bridge of Weir, Renfrewshire. Her staff were suspicious of the package and contacted Strathclyde Police.
The third package was addressed to Mr McBride at the Faculty of Advocates in Edinburgh.
It is believed to have been posted in Ayrshire before being found in a letter box by a postal worker on Friday and taken to a Royal Mail sorting office in Kilwinning, where police were contacted.
Det Sup Mitchell said: "The initial assessment was that they may have been a hoax. That being said, the investigation that followed was very important.
"We sent devices to specialists for forensic examination and, on the back of that, we now realise they were indeed viable devices."
He added: "They were definitely capable of causing significant harm and injury to individuals if they had opened them.
"It is important to say that there is no doubt that there is someone out there with information that can assist us and take this inquiry forward and the quicker the better."
Speaking at the same press conference at Strathclyde Police's Glasgow headquarters, Ch Sup Ruaraidh Nicolson appealed for the public to be "vigilant".
He said the packages were not targeted at the general public but said it would be "sensible to take precautions".
"If they receive something in the mail that they are unhappy about or they didn't expect to receive, then they need to think about phoning the police," he said.
Detectives are also investigating another package addressed to Neil Lennon which was found at a sorting office in Saltcoats, North Ayrshire, on 4 March but this has not been confirmed as an explosive device.
It is understood that specialist anti-terrorist officers are involved in the investigation but a source close to the inquiry said they were "not linking this to any terrorist organisation".
Lennon, a 39-year-old Catholic from Lurgan, County Armagh, has endured threats, abuse and violence since joining Celtic in 2000.
In January this year bullets addressed to the Celtic manager were intercepted at a sorting office in Glasgow. They appeared to have been sent from an address in Northern Ireland.
Mr McBride is one of the highest-profile QCs in Scotland and a well-known Celtic fan, who has acted for the club and Mr Lennon on several occasions.
Ms Godman has a lower public profile than Mr Lennon or Mr McBride, but is well known in political circles as an avid Celtic fan.
Until dissolution of the Scottish Parliament last month, she was deputy presiding officer and the Labour MSP for West Renfrewshire.
On her last day as an MSP she was pictured in the Holyrood chamber wearing a Celtic football top.