The 30 year old striker hit the target 11 times last term from 38 appearances.
The Northern Ireland international will official join the Millers when his current deal with Charlton ends on 30th June.
Speaking to the clubs official website - themillers.co.uk Washington spoke of his delight with the move.
“It’s great to be here, the manager and his coaching staff set their stall out very early in terms of their interest, This has always been a football club that me and my agent thought would suit me down to the ground in terms of style of play and what the fans expect from a player. I think it’s going to be a really good fit."
“I’d heard a lot about The Gaffer, as well as Richie and Hammy, too. It was nice to put a bit of personality and faces to the names and the Zoom meetings were everything I expected them to be and more.
“My vision aligned with theirs. I wanted to be back at this level, competing to play week in, week out and they think I can do that. I still think I have a lot to learn as well and I think they can help me to push on my game further, I’m excited to get going."