Meldrum-Jones also performed other sex acts on the boy "under the cover of darkness" on the 10-hour flight back to England days later.
A court heard the teaching assistant also sent the teenager "highly sexualised" messages once they were back in the UK but there was no more physical contact.
The incident only came to light in February this year when rumours which were circulating the school were brought to the attention of the police.
Meldrum-Jones gave no comment interviews to officers but pleaded guilty to five charges of sexual activity with a child at Warwick Crown Court on November 2.
She also admitted two charges of causing or inciting a child to engage in sexual activity.
Meldrum-Jones wept in the dock as she was jailed for two years and eight months at Coventry Crown Court.
The teaching assistant, who wore a black long-sleeved T-shirt and black trousers, was also handed a sexual harm prevention order for five years.
Sentencing, Judge Philip Gregory said Meldrum-Jones "must have completely lost control of her senses and been consumed with lust for this young boy".
He added: "It seems to me that you lost control of your senses as well as control of your physical urges.
"At the time you were a teaching assistant charged with responsibility for teenage children on a school trip.
"This should have been a wonderful experience but for one of them, the victim, it was an incident which has plagued him ever since because of the serious sexual misconduct of which you involved him.
"You're 37, he was 15. That's a substantial age difference, you and you alone are responsible for what happened.
"It would have been bad enough if it happened on one occasion but it happened repeatedly.
"And it didn't end there on the holiday because under the cover of darkness on the flight home, and this almost beggars belief, you engaged in similar conduct with him.
"Once you were back in the UK you exchanged explicitly text messages with him.
"It almost beggars belief that someone from your background, happily married with two children, should so lose control of your senses and judgement that you would permit yourself to behave in this way.
"You and your family need to understand that judges have to follow the law and have to implement it.
"I acknowledge the appalling humiliation to which you've been subject and the hell that your husband and children will suffer as a consequence of your absence."
The court heard Meldrum-Jones, who has a 12-year-old son and a 7-year-old daughter, was "overly familiar" with pupils at the school, which can't be named for legal reasons.
Prosecutor Stefan Kolodynski said the teaching assistant sent the boy racy text messages which were "geared to her arranging further sexual congress" with the boy.
But the "flirtatious texts" ended when "she realised what had gone on could not be repeated".
The court heard the teenage victim made disclosures to friends but only agreed to talk to police in February this year after a conversation with his mother.
Summarising his victim impact statement, Kolodynski said: "He says: 'I just feel horrible about it all, when I'm out I feel quite cautious because I don't want to bump into people who know what has gone on'.
"He said he feels very nervous. Every time he goes out he feels people are talking about him.
"When he's walking with his dog he likes to put his hood up because he always feels people are gossiping about him."
Simon Hunka, defending, urged the judge to spare Meldrum-Jones prison and give her a suspended sentence.
He added: "The reality is having read the references she has a particularly strong role in the upbringing of the children and is described by her husband as the cornerstone of the family.
"Her behaviour is so out of character given her life prior to last year.
"To engage in the behaviour that she did in the main body of an aeroplane, yet she did that and she is not a fool, she is not someone who has routinely engaged in that type of behaviour in the past.
"She suffers from depression and was diagnosed two months after this (incident).
"Depression can't be an explanation but when someone suffers from depression they lose that same sense of fear and they take decisions that others wouldn't ordinarily do.
"I can't explain away what she did but it sets in some context why this woman goes to such strange extremes."
An NSPCC spokesman said after the case: "Parents send children on school trips with the expectation they will be cared for by teaching staff.
"Meldrum-Jones abused that trust and must face the consequences of her grossly inappropriate behaviour.
"Her victim has struggled to come to terms with what happened and it is vital that children who are subjected to sexual misconduct, get the necessary support to move forward with their lives."
