Parcel bombs sent to Celtic manager Neil Lennon, a lawyer and a politician were "designed to cause real harm to the person who opened them'', police have said.
ESPN pundits on Lennon
Two suspect packages were addressed to Lennon and one to Paul McBride QC and former Labour MSP Trish Godman.
Strathclyde Police Detective Superintendent John Mitchell said sending the packages was a "despicable and cowardly act''.
The first one was found in Saltcoats, Ayrshire, on March 4 and the second was intercepted on March 26 in Kirkintilloch, East Dunbartonshire.
Two days later, on March 28, a parcel for Ms Godman, the former deputy presiding officer of the Scottish Parliament, was delivered at her constituency office.
The most recent package was intercepted last Friday at a post-box on Montgomerie Terrace in Kilwinning, Ayrshire, and was addressed to Mr McBride, who represented Lennon at Hampden during his recent dispute with the Scottish Football Association (SFA).
Mr 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.
"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 a press conference at Strathclyde Police's Glasgow headquarters, Chief Superintendent 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''.
He said: "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.''
Lennon, 39, has endured threats and abuse during his career and was forced to retire from representing Northern Ireland in international football after claiming he had received death threats from a paramilitary group. He was the victim of a street attack in the west end of Glasgow in 2008 and earlier this year he received a package containing bullets.
Celtic players Niall McGinn and Paddy McCourt, both from Northern Ireland, were also sent bullets.
Mr Nicolson said: "In terms of the general public, there is no danger, there is no risk. This is focused on high-profile people who have been in the media, who need to take sensible precautions.''
Mr McBride is one of Scotland's most-recognised QCs and is a well-known Celtic fan. Last week he accused the SFA of bias towards Rangers after assistant manager Ally McCoist and players Madjid Bougherra and El-Hadji Diouf all escaped bans after being charged with misconduct following an Old Firm Scottish Cup clash at Parkhead.
The SFA announced later it was considering legal action against Mr McBride over "unjustified and inflammatory remarks''.
Ms Godman, who is stepping down as an MSP, was deputy presiding officer of the last session of the Scottish Parliament and the Labour MSP for West Renfrewshire. On her final day as an MSP she was pictured wearing a Celtic football top at Holyrood.
Scotland's First Minister expressed his shock at the "disgraceful events''.
Alex Salmond said: "We will not tolerate this sort of criminality in Scotland, and as an indication of the seriousness with which we view these developments the Cabinet sub-committee met last Saturday to ensure that the police investigation has every possible support to come to a successful conclusion. We are confident that this will be the case.
"These disgraceful events should remind all of us who love the game of football of what unites us as a community. It is time to remember what we value in society, and unite to condemn those who use football as a pretext for their pathetic and dangerous prejudices.''
Scottish Labour leader Iain Gray said: "I am shocked and appalled at this sinister development. It is vital, though, that people keep calm and do not let the situation spiral out of control, as that would be playing into the hands of the extremists behind this vile act.
"It is outrageous that something like this should happen in Scotland in this day and age. Strathclyde Police must have whatever support they need.''
A spokesman for Celtic chairman Lord Reid said the club had been kept fully informed of events and should be making a statement later.
The chief executive of the Scottish Football Association said the news was "depressing and deplorable''. Stewart Regan said the SFA was "horrified and saddened'' by the attacks, adding that sectarian hatred was an "unwanted poison'' in football.
He said: "Scottish football should be a safe and entertaining environment for players, coaches and supporters. It must not be used as a platform for religious intolerance or hatred.''
UEFA president Michel Platini said: "It's a pity in football that we have these problems. We have to keep politics and religion out of football and sport, that is very important.
"It's a very bad thing that has happened to the manager of Celtic and the whole of UEFA support him. We have to do try to help football and to do something. With my heart I am with him."
Lennon's assistant, Johan Mjallby, revealed his close friend was focused on his job despite the threat to his safety.
Mjallby, who was speaking before Celtic's SPL contest against Kilmarnock at Rugby Park, told BBC Scotland: "He's in a good mood and all he wants to do is prepare the team for the run-in and talk about football. Neil's a strong character but it's still a terrible thing.
"It's not a distraction he wants right now but he loves his job as manager of Celtic Football Club and right now he just wants to prepare his players. Obviously it's not a nice thing and it's maybe in the back of his mind but he is professional and he loves his job.
"It's a good distraction having a game as he loves to be close to the players.''