The midfielder spent three years at Tannadice but leaves after their relegation from the Premiership.
Saints manager Tommy Wright told his club website: "Paul is underestimated - he's an aggressive player but has a lot of real quality too.
"His range of passing is excellent and throughout this career his attitude on the pitch has been great."
St Johnstone have already secured midfielders Blair Alston and Michael Coulson from Falkirk and York City respectively, while defeners Keith Watson is making the switch from St Mirren.
"We believe we've captured another good signing for the forthcoming season - our fourth - and I think in all four we are bringing quality and experience into the squad," said Wright.
"It not only improves the quality but also in terms of depth we are sitting, I believe, in a good position.
"I've always emphasised the point that it is the whole squad that has enabled this football club to achieve what it has these past few seasons and the addition of Paul will enhance that."
Paton joined United in the summer of 2013 from Partick Thistle, going on to make 90 appearances for the club.
He captained the side in the latter stages of last season and thanked the club's supporters "and everybody at Tannadice" on the club's website.
"There will always be a tangerine spot in my heart and I wish Dundee United every success in returning to the Scottish Premiership next season," he said.
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She told BBC Radio 4's Today programme that people should take more notice of their surroundings.
Measures such as the closure of railway stations in Munich on New Year's Eve would become more likely.
Such moves showed "prudence and proper caution" by authorities, she said.
Official guidance is that members of the public should be "alert but not alarmed" about the threat of terrorism.
But Lady Neville-Jones, former head of the Joint Intelligence Committee, said people were not as vigilant as they could be.
"I think being alert is very important," she said. "I am alarmed by the number of people I see wandering along the street entirely engaged in their mobile telephones and with their ears plugged in to music.
"They're not aware of their surroundings - you need to be aware of your surroundings."
When interviewer John Humphrys said that was "how we should be able to lead our lives", she added: "Maybe, but I do think you need to take some personal responsibility."
Two railway stations which were closed in Munich in response to a suspected terror threat reopened on Friday after German officials said there was no sign of an imminent attack.
Lady Neville-Jones said: "I do think we are going to have to get used to what we have seen yesterday in Germany - that is to say alerts which close places of public functions, and higher levels of security in big public gatherings.
"That is prudence and proper caution on the part of intelligence and the police authorities."
Authorities have a responsibility to take information seriously, even if the wider picture is not clear, she said.
"It's a very bold government or policeman who chooses not to take precautions in such circumstances," said Lady Neville-Jones.
"I think the population on the whole would prefer them to be cautious and occasionally have closed something that it turned out wasn't necessary, but how do we know, rather than take the risk of exposing people to dangers on which they have information, even if it's not complete and on which they can't necessarily totally rely."
But she said UK cities were unlikely to be locked down in the way Brussels had been over recent terrorism concerns.
She told Today: "I would hope that that would not be something that would happen in the UK.
"I do think that counter-terrorism and both the intelligence side of it and the policing side of it, and well done, are matters which are bred of long experience and of great skill and I think that in this country we do have both of those things and we have very close co-operation between both police and agencies and I think they understand how to use information.
"I don't think those skills are nearly so widespread on the continent. So I think we shouldn't conclude that what happened there is necessarily the technique that would be adopted here."
Paul Paton has signed a two-year deal with St Johnstone after leaving Dundee United by "mutual agreement".
[NEXT_CONCEPT]
Former security minister Baroness Neville-Jones says she is "alarmed" by people using mobile phones in public instead of being more alert to the risk of a potential terrorist attack.