Its £4.5m development of the former Stainsby filling station site, on the outskirts of the village, was turned down by councillors in June.
There were fears over traffic and the design of the building, which will be sited beside the main A149 coast road, near the Norfolk Lavender traffic lights.
But today West Norfolk council's planning committee approved the scheme by nine votes to three.
Lidl had appealed against the earlier refusal, arguing councillors were originally recommended to approve the scheme.
It has offered to install yellow hatched keep clear markings on the main road and has also re-designed the store, using more local materials.
A report to councillors said the store would create 40 new jobs and open from 7am - 10pm from Monday to Saturday, and 10am - 7pm on Sundays and bank holidays.
It said the supermarket would be built on the northern part of the site, with 129 parking spaces on what is currently a car wash and car dealership.
'The design of the development is said to be poor,' the report considered by councillors today goes on.
'It is not clear whether this is directed at the appearance of the building or to the site layout. In either case Lidl does not agree. 'The proposal is for the Company's latest generation of foodstore. Its appearance is simple, clean, functional and modern and it employs high quality materials and sustainable building
management systems. In relation to the layout of the site Lidl notes the following points.'
Heacham Parish Council objected. In its response to consultation over the store, it said: 'There are implications for traffic
delays at the 'Lavender Lights' due to traffic waiting to turn right from Heacham to access the store not having a space to queue in and, similarly for traffic crossing the junction from Hunstanton or turning left from Sedgeford. In addition, traffic implications remain for people living along The Broadway, Nourse Drive and Lynn Road.'
The Norfolk Coast Partnership also objected, saying the scheme would have 'an adverse impact' on the lansdscape.
Three letters were recdeived in support. One said: 'The people in Heacham (excluding parish council members) want greater choice
instead of having to travel to Hunstanton or King's Lynn.'
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