The midfielder succeeds Luke Murphy as captain, a decision which was greeted with warm applause from his team-mates.
"Abdul is a player the lads really respect," Davis told the club's official website. "He has the respect of the players and the staff and he is a great lad to have around the place. He has a strong personality and will grow into the role as well.
"It may well help with his discipline as well. He picks up some silly bookings at times and the extra responsibility will help him with that.
"I pulled the squad together and introduced Abdul as the new captain. They applauded that and congratulated him. That tells you, you have made the right decision. The lads had written skipper on his water bottle so he had an idea."
Osman will don the armband for Alex's home game with Rotherham on Saturday.