Zuniga can play in either full-back position and has 62 caps for his country.
The 30-year-old joined Napoli in 2009 from Siena, and played for four years under new Watford boss Walter Mazzarri.
He is the Premier League club's fourth summer signing, following centre-back Christian Kabasele, striker Jerome Sinclair and record buy Isaac Success.
Zuniga played four times for Colombia at the 2014 World Cup, and it was his challenge that caused Brazil forward Neymar to miss the 7-1 semi-final defeat by Germany.
The defender has appeared 125 times for Napoli during seven years at the Serie A club and spent a short spell on loan at Bologna at the start of 2016.
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He was also being assessed for post-traumatic stress disorder (PTSD).
Post-traumatic stress disorder is an anxiety disorder caused by witnessing or being involved in a frightening or distressing event.
People naturally feel afraid when in danger, but the legacy of some traumatic events is a change in perception of fear.
They may feel stressed or frightened in day-to-day life.
Any traumatic event has the potential to lead to PTSD including:
People will be generally affected within one month of the event.
There is no blood test for PTSD, it instead relies on the judgement of a doctor speaking to their patient about their symptoms.
There must have been an initial traumatic event involving a close brush with death or serious violence.
There are then four criteria which must be present:
"This has to impair day-to-day function," said Neil Greenberg, a defence professor of mental health at the King's College London.
"With properly skilled doctors it can be very easy to diagnose, it could take a few hours," says Prof Greenberg.
But he says doctors must have a good suspicion of PTSD before starting to diagnose someone, as patients may not bring up their trauma history.
It can also be a challenge because some people deliberately "overinflate symptoms", sometimes for financial reasons, while others seek to avoid the stigma of a PTSD diagnosis.
For many people, the symptoms will go away within a month - but others will need psychotherapy or, if that fails, medication.
Cognitive behavioural therapy can help change the way people think about the traumatic event in order to control fear and anxiety.
This involves going through the event in detail with a therapist.
Antidepressants, such as paroxetine, are used if psychotherapy does not work.
Prof Greenberg, who also works with the UK Psychological Trauma Society, says treatment is still effective many years after the incident.
However, after such a long time the symptoms are very unlikely to clear up without treatment.

Martyn Graham, 58, also seriously injured two other motorists in the crash of the A421 Bedford bypass on 12 January 2016.
A web cam in his cab showed the brake lights ahead for 17 seconds before the collision.
Graham admitted two counts of causing death by dangerous driving.
He also pleaded guilty to two charges of causing serious injury by dangerous driving.
A collision report said Graham had not reacted or braked at all, and the court heard the cause of his inattention remained a mystery.
He was not using a mobile phone, was not tired or ill, and had driven about two million miles over the previous years without incident.
Wayne Cleaver, prosecuting, told Luton Crown Court the couple who died were grandparents Martin Spratt, 70 and his wife Evelyn, 68, of Buckden, Cambridgeshire.
Davina Stubbs, 54, from Bedford sustained serious injuries and had to be cut free from her Vauxhall Corsa. She now suffers from post-traumatic stress disorder.
Danny Delasalle, 32 from Stevenage, who was driving a flatbed Transit van, had to wear a neck brace for three and a half months after the crash, the court was told.
Judge Philip Bartle QC said the crash had "devastating consequences" for those involved.
Graham said later he had no memory of the events leading up to the accident and could not explain why he had not braked.
Ian Bridge, defending, said Graham was thoroughly remorseful and thought of the accident every day and had sleepless nights.
Graham was also banned from driving for five years.
Watford have signed Colombia defender Juan Camilo Zuniga on a season-long loan from Italian side Napoli.
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