A formal offer document will be sent to shareholders in the next few days. An emergency meeting to discuss the offer - valued at around pounds 13m - will be held on or before 23 December.
Mr Anderson's consortium, which is being co-ordinated by accountants Stoy Hayward, has been battling against a bid led by Lawrie Lewis, the former chairman of Blenheim Exhibitions. This bid was higher at pounds 15m.
In a statement, Nottingham Forest chairman Irving Korn said: "The board feels that this offer [Mr Anderson's] gives the best overall terms for the club and its shareholders."
Mr Korn said he recognised that the offer from the Lewis consortium was more generous to shareholders "if viewed from the point of view of shareholders alone". However, he said he had not been informed as to whether Mr Lewis and his group, which includes ex-Tottenham chairman, Irving Scholar, would be continuing their interest.
The Anderson offer includes a pounds 13m cash investment for new shares and provides for the raising of additional funds this week. The existing 209 shareholders, who each own a single share in the club, will retain a 5 per cent stake.
Mr Anderson's consortium yesterday disclosed its other members, which includes a number of top businessmen.
It includes Charles Scott, head of Cordiant, which owns the Saatchi & Saatchi advertising agency and Nigel Doughty-Hanson of Doughty & Hanson, the London-based private client fund manager. Also involved is Tim Farr, a member of the family which used to control Home Breweries, the Nottingham brewer now owned by Scottish & Newcastle.
It is thought that Mr Anderson will take on executive duties at Forest, possibly as chief executive. It is not clear if this would mean him leaving Porterbrook, the train-leasing company which was taken over by the bus company Stagecoach in the summer in a deal which netted Mr Anderson pounds 33m
"We've got to consider what's best for the club," Mr Anderson said. "No decision has been taken and all this is a long way out. I'm very happy with Stagecoach."
Mr Anderson's group is talking with other possible investors. Further announcements may be made this week.
Most of the businessmen in the group have local connections. Mr Anderson, a Scot who was once on the books of Patrick Thistle, lives in Nottingham and supports the club. Nigel Doughty-Hanson hails from nearby Newark and is a season-ticket holder at the City ground. They brought in Charles Scott, who has no known Nottingham connections. Mr Farr is a Forest season ticket holder.
Stoy Hayward said yesterday that it was aware of a "golden share" rule which is a condition of the sale. This dictates that 80 per cent of funds raised from player transfers must be re-invested in new players. The new owners will not be allowed to sell the club for five years or change its name or the team's red shirts.