The 17-year-old chose to move to Emirates Stadium ahead of Manchester United, the Champions League and Premier League champions, as well as Everton after all three clubs expressed interest in the Wales Under-21 international.
"We're delighted to have signed Aaron Ramsey," Arsene Wenger said. "He is a young player who has shown huge potential with his performances for both Cardiff City and Wales at under-17 and under-21 levels. He is still only 17, but has already shown that he is a very intelligent and mature player with great quality.
"Although he mainly plays in midfield, Aaron is a versatile player and can also play across the defence. We are all looking forward to welcoming Aaron to the club for our pre-season preparations."