In a statement issued by the League Managers Association McLeish said: "I am extremely saddened to be leaving after such a short period but even so it has been a privilege to be manager of such a fantastic football club.
"Both parties entered into the relationship in good faith, however, there was a difference in the understanding of the development strategy of the football club and it was felt by both parties that we should part company.
"I want to thank the players, staff and fans for their support and wish Nottingham Forest the best of fortunes ahead."
Forest have said they will not be making any further comment.
The Al Hasawi family sacked the then manager Steve Cotterill within days of assuming control in the summer.
They promised an iconic name as a replacement but after being linked with Glenn Hoddle and several other "big-name" managers, they appointed former Reds coach Sean O'Driscoll.
Pat MurphyBBC Radio 5 live
McLeish took over on 27 December, that's not enough time to get a carriage clock.
At the heart of this is the January transfer window. We understand that Alex McLeish was promised around £3m to wheel and deal for players. The one that really annoyed him was George Boyd signing from Peterborough. He thought he had him for £500,000 but then the owners pulled out. Although Boyd passed a medical the owners said he had an eye problem so they would not be proceeding with it. McLeish thought that was ridiculous.
He guided a new-look Forest to a point outside the play-off places but was
sacked on Boxing Day
after an impressive 4-2 victory over Leeds United.
However under McLeish they have won just one of their six Championship matches, and are now in 11th place.
They are are six points adrift of Middlesbrough in sixth spot, having played a game more.
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