The deal includes the chance to earn $3 million in performance bonuses, the person said Tuesday, speaking on condition of anonymity because the agreement was not yet final.
Washington planned to announce the deal during a news conference Friday at spring training, the person said.
Wang, a right-hander who turns 30 on March 31, had spent his entire five-year major league career with the Yankees, who allowed him to become a free agent in December when they failed to offer a 2010 contract.
He made $5 million last year, when he was 1-6 with a 9.64 ERA and his season was cut short by shoulder surgery on July 29. He is not expected to be able to pitch until sometime between April and June.
Wang was a 19-game winner in 2006 and 2007, starting New York's postseason openers in both years, but his career was sidetracked when he severely injured his right foot while running the bases at Houston on June 15, 2008.
He missed the final 3½ months of the 2008 season, then allowed 23 runs in six innings over three starts when he returned last season. He went back on the disabled list, returned in late May to make three relief appearances and six starts before his season was ended by shoulder pain. Dr. James Andrews repaired a tear in the right shoulder capsule.