The supermarket chain – the fourth largest in the UK, was granted planning permission earlier this year to build on the former Gould's Electrical site in Bilston Street.
The Dudley Council-run car park next door will close on Thursday to make way for the development, and it is hoped the supermarket will be open for shoppers next year. The new store will have 90 car parking spaces and offer free parking for customers.
Councillor Patrick Harley, leader of the council, said: "We want to make people aware the council car park in Bilston Street will be shut from tomorrow so they can make alternative arrangements where necessary.
"This is fantastic news for Sedgley – it will create jobs, give residents an extra place for their food shop and also attract people into the village where they will hopefully visit other shops and businesses.
Aldi has over 990 stores nationwide and employs 40,000 people.