The former Cardiff City midfielder said after his switch was officially announced: "I am so happy to have signed for Arsenal. I am joining one of the biggest clubs in the world and can't wait to meet my new team-mates.
"He talked to me for a long time about the club and the plans for the future, which really excites me."
However, the teenager knows he cannot rest on his laurels if he is to cement a place in Wenger's first team at Emirates Stadium alongside the likes of Cesc Fabregas and Theo Walcott.
He said: "Arsenal is a club which always gives young players an opportunity at the highest level of the game and I am going to work my hardest to be part of future successes here."
Ramsey came through the youth ranks at Ninian Park, and admitted it was something of a wrench to leave the Wales club.
"It was a really difficult decision to leave Cardiff City, they are my local club with great supporters and I would just like thank everyone at Cardiff City for their support and help in my early career," he said.
"I will still look out for their results and there will always be a place in my heart for the Bluebirds."