The 48-year-old, who was initially asked to take up the reins for the Capital One Cup win over Peterborough and Sunday's 3-1 Barclays Premier League defeat by Liverpool, will continue in the role as the Black Cats run the rule over a series of potential replacements for Paolo Di Canio.
Sunderland confirmed the move on their official website on Monday afternoon, eight days on from the Italian's departure.
Confirmation, which was not unexpected, came as skipper John O'Shea ordered his team-mates to draw a line under the catastrophic breakdown of their relationship with Di Canio and dig themselves out of trouble.
The Black Cats remain rooted to the foot of the Barclays Premier League table after taking just a single point from their first six games and O'Shea, while confirming that the dressing room had played a part in the 45-year-old's demise, has insisted the players must re-group to prevent the club from being cast adrift.
He told the Sunderland Echo: "That was obviously done. But we have to move on now.
"Because of the position we are in in the league, we can't keep going back to it. We have got some difficult months ahead.
"Whoever comes in, whether it's Bally [interim head coach Kevin Ball] or a new manager, we have got tough times ahead.
"We have to stick together and if we keep going back to it, it will soon be too hard to pull back from where we are."
Sunderland turned in a much-improved display against Liverpool but ultimately came out of it empty-handed once again, and with United due to arrive on Wearside at the weekend intent on addressing their own losing streak, things could yet get worse before they get better.
The Black Cats are continuing to evaluate a series of potential candidates for the vacancy with Gus Poyet, Rene Meulensteen and senior professional development coach Ball, who has indicated his own interest in filling the role on a permanent basis, figuring prominently in the betting.
However, chief executive Margaret Byrne has revealed that discussions with several contenders have already taken place and talks with others will be held this week, and it appears an appointment is not imminent.
But should the club eventually opt to give the job to former Black Cats midfielder Ball, the decision would go down well with the players.
O'Shea said: "Without a doubt, he's made an impact. If it does happen, the players would be very happy.
"But we will wait and see what the club decides."
Ball launched his spell in charge with a 2-0 Capital One Cup victory over Posh on Tuesday evening, but was unable to repeat the feat against sterner opposition on Sunday.
Sunderland played a full part in the game, but were ultimately undone by the brilliance of the returning Luis Suarez and strike-partner Daniel Sturridge.
The latter gave Liverpool a 28th-minute lead when he bundled Steven Gerrard's corner home with his arm, and then set up the Uruguay international to score his first goal for the club since April with a perfectly weighted cross eight minutes before the break.
However, the Black Cats' response was hugely creditable and they got themselves back into the game within seven minutes of the restart when Emanuele Giaccherini struck from close range after keeper Simon Mignolet could only parry Ki Sung-yueng's shot from distance.
But the Reds held firm in the face of a concerted assault and secured their win with a minute remaining when Suarez and Sturridge combined superbly before the South American claimed his second of the game.
Ball was disappointed by the result, but hugely encouraged by the performance of his players in front of the watching owner Ellis Short.
He said: "That's something that whenever you come away from the Stadium of Light, no matter who is in charge, whatever the club, we have always got to see that.
"That's something that I would drum into the players in future, we must see that all the time.
"People must go away from here, irrespective of what happens, and away from home as well knowing full well that their team has put in a shift, and today, they can say that."