Aldi UK received planning permission for the store on land at 101 Field, off Ampthill Road, in the town.
The Aldi proposals would create 50 jobs locally and were intended to be completed by next summer.
But Tesco plc took legal action to seek a judicial review of the planning decision by Central Bedfordshire Council's development management committee.
"A judge has accepted there are arguable legal grounds to hear the case," according to a social media post by Independent Flitwick councillor Gareth Mackey.
To avoid store wars in the High Court, councillor Mackey said that "CBC and Aldi have agreed to concede the case" now.
"This is because of the judge's comments and the potential for considerable costs to the local authority should a defence of the decision be lost.
"Advice was take from Queen’s Council and approved by CBC's executive in reaching this decision.
"This relates solely to the disclosure of advice that officers received during the course of the application from a retail planning consultant and how the council publishes representations from third parties, including Tesco, on its website.
"There's a concern that the claimant, Tesco, didn't have an appropriate chance to feed into the planning application process, and for its comments and observations to be taken fully into account by CBC in its decision-making process.
"The application will be reverted to the council for redetermination," explained councillor Mackey.
"Interested parties, consultees and town councils will receive a further consultation letter inviting comment on the application in due course.
"It's likely that the applicant, Aldi, will wish to make extra submissions to its original application documents."
Both Flitwick Town Council and Ampthill Town Council supported the project, on a one-and-a-half acre site, with parking and an access.
The committee's original verdict was subject to the Secretary of State for housing, communities and local government releasing the area from the Green Belt.
If councillors decide to approve the application again or refuse it, interested parties will have an opportunity to challenge that verdict.
"I realise this is a deeply disappointing result to many residents," added councillor Mackey.
"It's my feeling there's a further opportunity to improve the scheme based on concerns I highlighted to the committee at the last hearing.
"I remain in support of the plans in general, as I feel the need for more retail choice outweighs the broad arguments against.
"But I hope concerns about traffic, noise, pollution, loss of Green Belt and access issues can be addressed and satisfactorily conditioned or mitigated at this stage.
"I'm also deeply disappointed that Tesco have chosen this course of action in what could be described as a cynical attempt to avoid competition.
"It damages the firm's brand and puts unfair pressure on their hard-working team at the town's store, who have to take the brunt of dissatisfaction with those who have no accountability locally."