Kenny was signed from QPR by manager Neil Warnock after playing last season in the Premier League whilst Ashdown also joined this summer from Portsmouth.
The 31-year old has been brought in to provide competition for Kenny and he is planning to do everything he can to win the number one shirt at Elland Road.
"It's a huge club and like all signings that come here it's exciting and it's a new challenge," he told the club's official website.
"I had a few options, but this is the best opportunity for myself and my family. I've had constant phone calls from the manager which is a good way to get to know someone.
"Once he'd told me about where he wants to go with the club, it's everyone's ambition for where they want to go.
"I've always had challenges. I've always played with and behind some good players and I've always pushed."