Andrew Wilbur, originally from California, has been married to a Scottish woman for six years but now no longer meets the criteria to stay here as their household income in the past year did not reach £18,600.
The income threshold was only introduced on marriage visa applications in July this year as part of a Government crackdown on immigration and sham marriages.
The move was aimed at ensuring spouses are able to support themselves while in the UK, but Mr Wilbur claims it is also hitting non-criminal, hard-working couples who simply have not earned enough.
The 32-year-old was due to start work at the university on a temporary basis, but now he and his wife, Laura Francescangeli, 34, have booked flights out of the country ahead of his student visa expiring on October 7.
Mr Wilbur, who has a PhD in human geography from Glasgow University, said: "I never realised I wasn't going to be able to stay here.
"It's been a shock, especially in light of being offered a job – basically that was my financial situation sorted for the short term.
"We've booked a flight to Italy on October 2. Laura's parents live there and I'm going to help out her family a little bit and basically buy some time to apply for other jobs.
"Because of my situation, I'm not going to be looking at jobs in the UK. I'll probably have to look in the US or somewhere else in Europe."
He added: "We've built our life here. We have quite a lot of family in Glasgow and lots of friends and all of my professional contacts are here.
"I think it will prove quite a challenge to insert myself somewhere new and try to establish myself again."
Ms Francescangeli said she felt "sad" there was nothing she could do to help her husband.
She said: "I'm just so shocked we have to leave. I feel so helpless. He's been married to me for six years and it doesn't seem to count for anything.
"This is our home. Our friends and family are here - and all the things I'm used to. Obviously I could stay, but we want to be together and don't have any other option but to leave the country to do that."
Mr Wilbur approached the UK Border Agency to apply for a Further Leave to Remain (Marriage) visa when he was offered the teaching position at the university.
However, he was told that, from July 30, applicants must meet the minimum household income of £18,600 in the 12 months prior to the application.
The couple's income did not come close to this as Mr Wilbur had been studying and his wife had been on Jobseeker's allowance in between visiting Italy to care for her father who is ill. He explained their situation to officials and told them he had been offered work, but was informed it did not make a difference.
He claims he and his wife may have to be separated for a period if he is forced to return to the US to work, adding: "We have a green card pending for Laura, but there's a very real possibility we could be split up for a while. It's horrible and neither of us is very proud of the fact we're having to turn up on our parents' doorsteps like this."
Mr Wilbur's university lecturer, Professor Christopher Philo, said it was strange the graduate was being asked to leave the country when he has so much to contribute to higher education in Scotland.
Mr Philo said: "Andrew is a gifted scholar and researcher and has contributed fully to the life of our school at Glasgow University – undertaking teaching of undergraduates, as well as running events and participating in research groups. He has been educated and trained in the UK and is fully committed to contributing to the UK higher education sector.
"I do not know the technicalities of the case, but on the basic 'human' side, given Andrew's record and potential in UK higher education, it does seem like a strange decision for the authorities to have reached."
A UK Border Agency spokesman said: "We do not routinely comment on individual cases. But we are clear all applications for settling in the UK must meet the requirements of our immigration rules and those that do not may be refused."