The wing-back has sign pro terms after extended trials last season following a departure from Chelsea.
Washington is the son of former Chelsea fullback and Champions League winner Ryan Bertrand, who is working closely with him.
“I think it's been such an honour to have him take me through clips and walk me through games that I've played,” Washington told Arsenal.com.
“He's really passionate about making me a better player and probably a better version of him. We might have a bit of an argument about it but you get it out of him.“
Arsenal career targets
Washington, 18, also laid out his ambitions with the Gunners.
He continued, “My ambitions are just to prove in every game you play and every training session you have. I think football is all about proving. I feel like just because I've signed this contract doesn't necessarily mean that I've made it.
“I think I've got a lot to prove and I'm looking forward to doing that. Hopefully, obviously, the coaching staff can see that through my game.
“It's a very welcoming club. From day one when I came here, I felt really welcomed. That goes from the staff to the players.
“I think it's a really big club, obviously. The club are always striving to win trophies. I'm just looking to be an addition to that and see what I can offer the club.”