She said in an earlier statement: "No one should ever have to go through what he did and it will take him time to heal and recover. He is very overwhelmed."
The couple have hired a leading international criminal law barrister to begin the arduous process of overturning Hedges' conviction for spying while also trying to sue the United Arab Emirates (UAE) for unlawful imprisonment.
Hedges was arrested at Dubai airport in May as he tried to leave the UAE after two weeks spent researching his doctorate on security in the region in the wake of the Arab spring. He was convicted of spying for MI6 last week after a five-minute hearing and sentenced to life in jail. He was freed on Monday under the terms of a presidential pardon although his conviction remains on his record.
Rodney Dixon QC, who was hired by Tejada while her husband languished in solitary confinement, told The Telegraph: "We are so very relieved Matthew is back home. In due course we will consider all legal options and remedies to clear his name of this false and unfounded conviction, and to obtain relief for his extended period of unlawful and arbitrary detention."
Dixon added: "Legal actions in both the UAE, although very limited, and internationally - including before the UN - will be explored."
Hedges is desperate to clear his name, backed up by the insistence of Jeremy Hunt, the Foreign Secretary, that there was "absolutely no evidence" to suggest the PhD student had worked for MI6.
Yesterday Hunt, who helped to negotiate the release, tweeted: "Welcome home Matt Hedges! The whole country is relieved and delighted to have you home."
The UAE authorities forced Hedges into a video confession before announcing the presidential pardon. The video was shown to a handful of selected journalists but not released publicly. In it Hedges confesses to being a "captain in MI6" although no such rank exists in the British intelligence service.
The jailing of Hedges had plunged the UK and UAE into a diplomatic crisis with MPs calling for a withdrawal of military support and some academics electing to boycott the Gulf state.
The National, the English language newspaper which is based in the UAE and is well connected, claimed Hedges had begun spying for MI6 after landing a job with a UAE-based security consultancy. "What at first appeared to be a bookish fascination with all matters security now appears to be the start of a short career as a spy for British security services," claimed the newspaper.
The National claimed he had been arrested after a "two-week mission where he tried to obtain information about sensitive military procurement and specific security details of senior royal figures."
The UAE has not produced the evidence it claims to hold against Hedges that includes material said to have been held on his laptop and mobile phone.
Security experts point out that the UK and UAE are allies and that MI6 has no need to spy on the Gulf state or its ruling class. It is possible that Hedges - in questioning locals about security in the region for his PhD - had alarmed individuals who had reported their suspicions to the authorities.
This article originally appeared on the Daily Telegraph.
