The Greens, who have spoken out repeatedly on this issue, are claiming a victory that would put an end to concerns that Scotland would be forced to take unqualified teachers from other parts of the UK.
The bill would have forced the General Teaching Council for Scotland (GTCS) to register individuals as qualified teachers, even if they did not meet professional standards.
Teachers are to be made exempt from new laws on the "recognition of professional qualifications and experience" from the rest of the UK, similar to an exemption already in the bill for Scottish legal services.
The change came after work by Scottish Green education spokesperson Ross Greer MSP with former leader of the Green Party of England and Wales, Natalie Bennett, who now sits in the House of Lords.
Ms Bennett moved the first amendment to exempt teaching standards from the bill, which forced the UK government to come forward with new proposals, including this exemption. This new amendment has been agreed by the Lords.
Mr Greer said: “The Internal Market bill is a direct attack on Scotland’s democracy and in breach of international law. The UK Parliament should reject it entirely, but given that is unlikely, I’m glad the Greens have secured new protections for Scotland’s centuries-old independent education system and the high standards of our teaching profession.
“That the Tories were prepared to allow individuals to teach in Scottish schools despite our teaching regulator regarding them as unqualified was frankly depressing. It was unfortunately no surprise though, coming from a Westminster government led by a man who thinks devolution was a 'disaster' and who is now doing all he can to undermine it.”
The GTCS said it “welcomed changes to the UK Internal Market Bill that will see the teaching profession and teaching services excluded from its provisions”.
Ken Muir, GTCS chief executive and registrar of GTC, said: “We would like to thank everyone who has helped get us to this position. From the parent groups who came together to lobby our on behalf to the politicians of all hues who listened to our concerns, in particular Michael Russell MSP, Ross Greer MSP, Baroness Bennett of Manor Castle and Carol Monaghan MP, all of whom have driven GTC Scotland’s message in political spheres.
“Finally, we would like to thank teachers and parents who helped galvanise support by writing to their local representatives. Education in Scotland is carried out in partnership and this was indeed a magnificent team effort.”
GTCS Council convener David Innes said: “I welcome the progress we have made on the Internal Market Bill. This has always been about safeguarding the system that maintains high teaching standards in Scotland and protecting the quality of teaching that our children receive and deserve.
“There are still a few stages to go through before we can be fully satisfied that the teaching profession and teaching services will be exempted from the Bill, but the signs are much more positive that this will be the case.”