James Lynch, co-director of human rights organisation FairSquare, who is also a former British diplomat in Qatar, said the incident had been a “horrendous ordeal” for Mr Guerrero Aviña.
He said: “I don’t underestimate how much of a toll this experience will have taken on him.
“Amongst other things, he went through a terribly unfair trial that UN experts have raised serious concerns about, and was deprived of his HIV medication in prison.
“I hope he can find time and space in the coming weeks and months for rest and recovery.”
Mr Guerrero Aviña’s family previously told the BBC that he was using Grindr in February and arranged to meet a man at his apartment in Doha.
However, when he went to the lobby to meet the man, he was detained by Qatari police officers, despite having no previous criminal record, they said.
His brother claimed that Mr Guerrero Aviña had methamphetamine planted on him and was then “pressured” into accepting it was his.
At a hearing in Doha in June, Mr Guerrero Aviña was found guilty of being in possession of an illegal substance and given the fine.
After an unsuccessful appeal, he has now been given permission to leave the country.
Homosexuality is illegal in Qatar, with punishments including fines and prison sentences.
BBC News has contacted Qatari officials for comment and is awaiting a response.
A Qatari official has previously insisted that his arrest was on the basis of possession of illegal substances and that “no other factors were taken into account”.
They said Mr Guerrero Aviña had been treated with dignity and respect, and that a test had confirmed the presence of drugs in his system at the time of his arrest.
Amnesty International described his treatment in custody and trial as “utterly horrific”.
The Mexican Ministry of Foreign Affairs said that both British and Mexican diplomatic staff accompanied Mr Guerrero Aviña to Hamad International Airport in Doha for his flight back to the UK.
They also thanked the British government for its support during his time in detention.
