The panel found Pupil A to be a credible, reliable witness and agreed with his version of events.
The boy was convinced he was in love with Wilson and they met several times outside of school.
After the trip they continued to meet outside of school and Wilson also had 'one to one' meetings with him in her office.
They sent each other text messages and drank cider together.
In September 2015 the school's head teacher heard rumours of the affair with the pupil.
Miss Wilson was interviewed but denied any improper behaviour and no further action was taken.
The teacher told Pupil A to erase their emails and texts and deny their relationship, the panel heard.
But it came to light when a second pupil, Pupil C, said he would reveal the affair unless Wilson had sex with him too.
These emails were reported to both the school and the police. The allegations were further investigated and Miss Wilson was sacked in May 2016.
Panel chair Polly O'Malley said: "In light of the panel's findings, there was evidence that the teacher's actions were deliberate and continued for a significant length of time despite her understanding that her behaviour was inappropriate.
"There was no evidence to suggest that the teacher was acting under duress.
Striking her off from the profession, she added: "These behaviours include serious dishonesty and serious sexual misconduct.
"The panel has found that Miss Wilson engaged in sexual activity with Pupil A on one occasion, including oral sex and sexual intercourse.
"Additionally the panel has found that Miss Wilson encouraged Pupil A to hide their relationship and lied about it herself when an investigation into the allegations was undertaken by the school.
"I have considered whether allowing for no review period reflects the seriousness of the findings and is a proportionate period to achieve the aim of maintaining public confidence in the profession.
"In this case, there are three factors that in my view mean that a no review period is proportionate and in the public interest, maintaining public confidence in the profession.
"These elements are the dishonesty found, the sexual misconduct found and the lack of insight.
"I consider therefore that a prohibition order with no review period is required to satisfy the maintenance of public confidence in the profession.
"This means that Miss Eleanor Wilson is prohibited from teaching indefinitely and cannot teach in any school, sixth form college, relevant youth accommodation or children's home in England.
"Furthermore, in view of the seriousness of the allegations found proved against her, I have decided that Miss Eleanor Wilson shall not be entitled to apply for restoration of her eligibility to teach."
Miss Wilson was not present or represented at the hearing. The name of the school was not revealed to protect the identity of the boy.