The finding increases the total number of such genes to 15, researchers said.
"This unprecedented analysis provides the most comprehensive genetic profile of glaucoma to date," said Paul A Sieving, Director of US National Eye Institute (NEI).
Glaucoma is a group of conditions that damage the optic nerve, a bundle of nerve fibres connecting the eye to the brain. Primary open angle glaucoma, the most common type, was studied in this analysis.
If detected early, vision loss can often be prevented with surgery or eye drops to lower pressure. The most common culprit of irreversible vision loss, glaucoma affects about 60 million people worldwide, according to the researchers.
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The underlying causes of primary open angle glaucoma remain poorly understood, but likely involve the interaction of many genes with environmental influences.
The researchers compared the DNA of 3,853 people of European ancestry with primary open-angle glaucoma to a similar group of 33,480 people without it.
Additional analyses of datasets from Europe, Australia/New Zealand, and Singapore also found associations between glaucoma and these gene variants.
All three genes are expressed in the eye. TXNRD2 and ATXN2 are active in the optic nerve.
Scientists had already identified an association between FOXC1 and glaucoma, but only in rare cases of severe early-onset glaucoma.
The TXNRD2 gene makes an enzyme that protects mitochondria against oxidative stress - the build-up of toxic byproducts from normal metabolism.
"This is the first direct report to show the association of a gene linking oxidative damage to glaucoma," said Neeraj Agarwal, a programme director at NEI.
Little is known about the normal function of ATXN2, researchers said. Mutations of the gene are implicated in a rare disorder called spinocerebellar ataxia 2 that causes loss of balance and coordination.
It is the third gene associated with both glaucoma and amyotrophic lateral sclerosis (ALS), also known as Lou Gehrig's disease.
However, there is no evidence that people with glaucoma are at greater risk of developing ALS.
The study was published in the journal Nature Genetics.