The Germany goalkeeper left Bayer for the Gunners yesterday for a fee rising to €25m.
"I enjoyed the time in Leverkusen from the first to the last day. It makes me very grateful that the club was willing to give me the number 1 status as a 19-year-old," said Leno.
"After a fantastic seven years, I will now continue my way in another, very exciting league.
"But I am sure that we will see each other more often on the international (European) stage."