Smith wore the captain's armband in the 1-0 Boxing Day defeat to Wigan which sparked rumours that Geremi, who also started the game, had been axed.
However, Cameroon international Geremi is set to depart for the African Cup of Nations in January and Allardyce has said Smith will take up the vacant captain's role.
"It's a permanent decision for now because obviously Geremi is going away to the African Nations," Allardyce told Newcastle's official website.
"We need to establish for a while somebody who can captain the side on a regular basis with the attitude, desire and commitment that Alan shows.
"We need to see that from all the players because we cannot win a Premier League match without that level of commitment from everyone."