City have used three keepers in the Premier League this season, with Kasper Schmeichel and Andreas Isaksson also having a spell between the sticks. Isaksson has started the last four league matches, but Hart will return to the side for Saturday's trip to Aston Villa.
Eriksson acknowledged that his decision could prompt Sweden international Isaksson to consider his future at City.
"On Saturday, Joe Hart will play and will be my No.1 for the foreseeable future," Eriksson told the club's official website.
"I have had talks with Andreas today and obviously he's not very happy. I had to make a choice and for this moment I've made the choice in Joe Hart.
"I don't know if Andreas wants to leave or stay and fight for the place, but I told him it's very much up to him.
"I will not be surprised and I will understand it if he wants to leave.
"It was important and for the players to come up with this decision before the window opens in January."