The Hungary international has been without a club since his deal with Liverpool expired in the summer.
Bogdan told the club's website: "I'm really happy to be back at a club that means a lot to me.
"My family and I really enjoyed our time here last season and when the opportunity arose to sign it didn't take me long to think it over.
"I've been training on my own and with a few clubs, waiting for the right opportunity.
"It's been good to see a few old faces and meet some new ones. Now I just want to work hard and hopefully give the head coach something to think about."