The French centre-half will replace William Gallas who is out of contract at the Emirates.
Arsene Wenger agreed to a €8.5 million fee with Lorient after weeks of haggling and having two other bids knocked back.
Koscielny, 24, will sign a four-year deal worth £25,000 a week and form a pair with Belgian international Thomas Vermaelen.
A Lorient insider
told The Sun: "The clubs have a deal in principle and an announcement
should be made in the next few days."
Read all about the World Cup 2010 at worldcup.soccerway.com