The House of Commons Scottish Affairs Committee said it was necessary to address demographic challenges and fill skills gaps in areas including health and finance.
The committee’s report was published just days after the Scottish Parliament’s Devolution Committee said UK Government policy was ‘’seriously restricting’’ the ability of universities and colleges to attract overseas students.
Scotland’s Europe and international development minister Humza Yousaf has urged UK Immigration Minister James Brokenshire to rethink his position.
There is cross-party support at Holyrood for replacing a scheme that allowed overseas graduates to work in Scotland for two years after completing their studies, abolished in 2012 by the UK Government.
The Scottish Affairs Committee said its removal had made Scotland less attractive, citing an 80% drop in non-EU students remaining in the UK after graduating.
Current visa arrangements mean international students struggle to find a job after graduating within the four month time-scale and minimum-salary thresholds “are not reflective of graduate salaries in Scotland”, the committee found.
It heard businesses have also been put off sponsoring students as current arrangements are “bureaucratic, costly and time-consuming”.
SNP MP Pete Wishart, chairman of the committee, said: “We currently have a situation where people come to Scotland from around the world to spend three or four years here being educated and becoming settled in our society.
“Then we raise unnecessary barriers preventing these talented individuals from staying and contributing to our economy.
“There has been an almost universal call for change and the UK Government must give assurances that it will take heed and give proper consideration to reforms.”
Both committees want the Scottish and UK governments to work together on the issue, as recommended by the post-referendum Smith Commission on further devolution.
The Scottish Affairs Committee also called for a review that would consider extending the period allowed for graduates to find work, reform to sponsorship rules and regional salary thresholds.
Mr Yousaf said: “This report adds to the growing pressure on the UK Government to reconsider the post-study work visa route to Scotland and take action to address our needs.
“As the committee has found, Scotland’s immigration needs are different to those of the rest of the UK.
“The Scottish Government believes that an improved post-study work visa route would help to address these needs and would be an important economic lever of great benefit to Scotland.”
A UK Government spokesman said: “We have been clear that we will examine any evidence which the committee, or other interested parties, might produce about the effectiveness of post-study work schemes and any suggestions they have for further improvements.
“The UK has excellent post-study work opportunities for students who wish to stay and work after graduating.
“Graduates can stay if they get a graduate-level job, get an internship or become a graduate entrepreneur.”