Washington, 29, has primarily been a special teams contributor in each of the last two seasons since signing with the Patriots.
Yates, 28, has been a valuable reserve at center and guard, filling in as a starter in seven games in 2008.
Both players were entering the final year of their contracts.
Washington was scheduled to earn $800,000, with a $57,000 workout bonus. His salary cap charge was $1.08 million.
Yates was scheduled to earn $650,000, with a $32,000 workout bonus. He did have an escalator in his contract that could have upped his salary by another $200,000. Not counting the escalator, his salary cap charge was $790,600.