The former Tottenham Hotspur full-back is unlikely to be cleared in time to play against Everton at the weekend.
Capped 53 times by Sweden, Edman will be known best amounst Premiership supporters for his screamer of a goal against Liverpool back in 2004/05.
Manager Steve Bruce was pleased with the capture. He said: "Finding a left back was always going to be a transfer priority and Erik is a top international who has experience of the Premier League. He knows what this league is all about, and has all the attributes to become a big success at the club.
"He has a fantastic left foot and decent pace, is good in the air, brave and reads the game well.
"It's not often such experienced left backs of this quality become available and I'm not surprised so many other clubs have been interested in him. I'm delighted he's chosen to come to us."