Recent reports speculated that McLeish was considering his future at the City Ground after little over a month at the helm.
The Scot was left frustrated after missing out on several transfer targets last month - most notably Peterborough winger George Boyd whose move to the east midlands was scuppered by a failed eye test.
And a bad week for McLeish was capped on Saturday with a 2-1 defeat at his former club Birmingham, where both Blues goals were scored by another player he tried to sign - Chris Burke.
It is thought the reason behind McLeish's decision to leave Forest is interference from the club's Kuwaiti owners, the Al-Hasawi family, in team affairs.
McLeish, who replaced Sean O'Driscoll as manager on December 27, said via a statement on the club's official website, nottinghamforest.co.uk: "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 and I want to thank the players, staff and fans for their support and wish Nottingham Forest the best of fortunes ahead.
"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."
When the Al-Hasawis completed their takeover of the club in the summer they outlined a three-year vision to get Forest back into the Barclays Premier League.
However, after a 4-2 home win over Leeds on Boxing Day left the Reds within touching distance of the play-off places, they changed their plans to target top-flight football this season.
The surprising decision to sack O'Driscoll was made that evening with the Kuwaiti's stating their intent to appoint a manager with Premier League experience.
Former Birmingham and Aston Villa boss McLeish was hired the next day but the Scot, in a brief 40-day tenure, won only one of his seven matches in charge and lost five.
Reds chairman Fawaz Al-Hasawi said: "I'm bitterly disappointed - as is Alex - that it has not worked out as we had hoped when he became our manager and I would like to put on record my thanks for his services to the club and wish him every success in the future."
McLeish's departure is the latest drama in a turbulent season at the City Ground.
Only last month the Al-Hasawi family caused outrage by sacking long-serving chief executive Mark Arthur and dismissing Reds legend Frank Clark from his ambassadorial role.
Chief scout Keith Burt was also given the boot along with Arthur and Clark.
McLeish leaves Forest 11th in the Championship table and six points adrift of the play-off places ahead of Saturday's trip to Bristol City, who recently appointed O'Driscoll as manager.