Victims will be paid $25,000 following a legal fight by campaigners.
Along with more than 30 other US states, Virginia once operated a sterilization program for individuals deemed undesirable or mentally unsound.
More than 8,000 Virginians were operated on between the 1920s and 1970s.
Virginia’s program was said to be the model for the Nazi eugenics policies introduced by Adolf Hitler when he aspired to create a master race.
Several countries practiced forced sterilization during the 20th Century, including Sweden, Canada and Japan.
In the US, about 65,000 Americans were sterilized in 33 states.
More than a fifth of those sterilized in Virginia were African Americans.
Two-thirds were women, many of whom went in for other procedures and were unaware of what was happening to them.
In 1927 the US Supreme Court upheld Virginia’s Eugenical Sterilization Act law. It remained in force until 1979.
The state issued an apology over the policy in 2001. Campaigners say there are only 11 known surviving victims of the program.
The compensation deal was welcomed by 87-year-old victim Lewis Reynolds.
“I couldn’t have a family like everybody else does,” he told the Associated Press news agency.
“They took my rights away.”
Virginia is the second state, after North Carolina, to approve a compensation package for victims who are still alive.
In 2013, North Carolina legislators agreed to pay $50,000 to surviving victims – thought to number about 1,800.
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