The ruling follows a test case brought by a north Wales schoolgirl against a former county council - one of four similar appeals from around the UK.
The case brought into question the legal status of dyslexia in the eyes of the law and whether failure by schools to recognise the condition and provide appropriate teaching, can give rise to grounds for a personal injury claim against the authorities involved.
Rhiannon Anderton - a pupil at the Bryn Coch Primary School from September 1983 to July 1990 - claimed her head teacher failed to recognise that she suffered from dyslexia.
But the Appeal Court ruled in November 1998 that circumstances such as this could not give grounds for a claim for damages for personal injury.
On Thursday, however, in a unanimous decision the Law Lords held that, if the system fundamentally failed a child in his or her education, then the victim had the same right to seek compensation as in the case of any other professional such as a lawyer, doctor or financial adviser.
One of the four cases involved Pamela Phelps, whose £45,650 High Court damages award over the London Borough of Hillingdon's failure to diagnose her dyslexia was taken away after a Court of Appeal ruling in 1998.
This latest judgement by the House of Lords restores Ms Phelps's damages award and opens the way for the other claimants to proceed with their actions.