Beavers accepted the 20-year plea agreement Tuesday, the same day he faced trial on the aggravated sexual assault charge.
Investigators say the victim, who is now 82, was asleep when Beavers broke into her Arlington home and attempted to rob her, then raped her when she said she didn't have any money.
DNA results from a national database matched Beavers in January 2009. His DNA had been entered into the system when he was in prison for assaulting a relative.