The 27-year-old, acquired from the Pittsburgh Pirates last month for a player to be named, went 8-15 with a 5.72 ERA in 29 starts last season. He has allowed 443 hits over the last two seasons, sixth-most in the majors.
He gets $3.5 million next year, and the Nationals receicve a $5.5 million option for 2011 with a $750,000 buyout.
Arizona also tendered contracts for next season to four arbitration-eligible players: shortstop Stephen Drew, second baseman Kelly Johnson, catcher Miguel Montero and pitcher Joe Saunders.
The Diamondbacks did not offer contracts to outfielder Ryan Church, utilityman Augie Ojeda and pitchers Blaine Boyer and D.J. Carrasco, making them free agents.