After a successful trial period, Bramall has completed a transfer to Arsenal from non-league Hednesford Town, who play in the seventh tier of English football.
The move was finalised on Tuesday morning but Oxlade-Chamberlain has spoken of his first meeting with the 20-year-old, who has been training with Arsenal since before Christmas.
He told the club's official website: "I was training on the side of the pitch with the fitness coach so I was looking over and then I saw him training, so I asked someone about him and they me a story and obviously it made me think wow. To be where he was a couple of weeks ago, and then to be training with the Arsenal first team, I was thinking he must be in dreamland over there. I paid close attention to him and saw some really good signs of things - you can see why we wanted to sign him.
"I was very encouraged by his story and quite inspired to see someone that's been given that opportunity and he was proving himself and holding his own. It was great, and then I chatted to him after training and he was just a really good lad and a top boy. He was generally just delighted and surprised at the same time, to be in the position that he was.
"He was really humble about it as well, which is always nice to see. Straightaway he seemed like somebody I wanted to help, and wanted to see do well."
Crystal Palace and Sheffield Wednesday had also been keen on Bramall before he attracted interest from Arsenal.