Former Scotland international McAllister made almost 300 appearances for Leeds during a six-year spell and will meet the players for the first time on Wednesday.
"When I was first approached on Sunday night I could not quite believe it but there was no hesitation in saying yes," he said.
"It is a great honour to be back at the club and I just cannot wait to be back in amongst it.
"I quite simply played my best football while at Leeds United, I was in my prime, we managed to win the First Division which was a great feat and I have nothing but great memories, fantastic times.
"There is no doubt in my mind that the Leeds fans are among the best in the world. I have been fortunate to play in front of them and I know that when they get going, Elland Road is an intimidating place to play and that is what we have got to create in the eight or nine home games we have left.
"It is a long-term project here at Leeds, a lot of work has already been done to get them back into the position they are in after their well documented problems and the place is certainly moving forward.
"When a new manager is appointed late in January, normally they are picking up the pieces from somebody being a failure but this is a winning side which has put itself in a fantastic position so I am joining a winning club which is already going forward."
McAllister was a member of Howard Wilkinson's Football League title winning side of 1992 and formed part of a terrific midfield that included Gordon Strachan, David Batty and Gary Speed.
He also enjoyed spells at Motherwell, Leicester, Coventry, and Liverpool, making over 700 career appearances and winning 57 international caps.
His honours include a League Cup winners medal, an FA Cup winners medal, a UEFA Cup success, and he was part of Liverpool the side which won the European Super Cup in 2001/02.
His previous management experience came at Coventry City in 2002/03.
McAllister is understood to have been in talks with Ken Bates since it became known that Newcastle United were interested in Dennis Wise late last week.
McAllister was a huge odds-on favourite to be named as the next manager following rumours he was in talks with the club this morning.