Walker was killed by lethal injection at 9:24 p.m. EDT, the Richmond Times-Dispatch reported.
Walker had had two requests for a stay before the high court. Both were rejected, with a court spokeswoman saying Justices John Paul Stevens, Ruth Bader Ginsburg and Sonia Sotomayor said they would have granted a stay, the Times-Dispatch reported.
Walker, 37, was convicted in 1998 of shooting and killing two men in separate incidents. Virginia law allows for execution of someone who commits two premeditated murders during a three-year period, the newspaper said.
Walker killed Stanley Beale, 36, Nov. 22, 1996, and Clarence Elwood Threat, 34, June 19, 1997.
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