The firms have beaten off competition from five other rivals to make the shortlist and will now work up detailed bids before a winner is chosen by Bolton Council in August.
The academy, formerly known as George Tomlinson School, will accommodate 950 pupils of 11 to 18 years old.
Bolton Council’s Executive Member for Children’s Services, Councillor Nick Peel, said: “Both companies have a wealth of expertise and experience and both their bids were really impressive.
“We are now looking forward to going through the final plans and selecting a preferred bidder.”
Once the winner is chosen, the school will benefit from a complete rebuild, including a new sixth form college, with work potentially beginning early next year.