The Uruguayan has opted to give the 28-year-old a chance to redeem himself following a conversation with his backroom staff, and has urged fans to get behind the defender
The full-back was close to leaving the club under former boss Paolo Di Canio after Bardsley's visits to casinos came to light.
Bardsley then appeared to mock Sunderland's opening-day defeat by Fulham and was subsequently suspended, but Poyet has decided to give the player a fresh start under his tenure.
Poyet told The Shields Gazette: "I have decided, with the backing of the club of course, that [Bardsley] is a part of the club and he is available to play.
"I ask the fans, with respect, to please give him a chance because he could be very, very important for us.
"He is very happy - delighted - to have another chance. He knows what he did was wrong, but it is in the past so let’s all try and put it behind us.
"Of course, he needs to make sure there are no more mistakes because then it would be impossible, but he will have a chance, and he could play an important part."
Bardsley is back training with the first team after recovering from a broken foot, an injury he suffered whilst playing for the Under-21s in August, and is available for selection to face Swansea City this weekend.
Poyet added: "He is fit now. I will make a final decision tomorrow over who will go to Swansea. Everybody will come in ready to travel, and I will decide then.