The French international was part of the second-best defence in the Premier League last season as the Gunners secured a fourth-placed finish.
Adams now believes that Koscielny plays with the same doggedness as his former defensive partner.
"He reminds me a lot of Martin Keown," he told the club's official website. "He's very tenacious. I hate labelling people because Martin Keown was one of the best we've ever had, but there are similarities there, the way Koscielny marks and his last-ditch tackles.
"To put Koscielny in the same category is an enormous compliment I think."
Arsenal start the new Premier League campaign at home to Aston Villa on August 17.