The Amazon Fresh store is the chain's 16th branch in London and has opened in the unit on the corner of Southwark Street and Sumner Street formerly occupied by Joy.
Customers must scan a barcode displayed in the Amazon app to open a barrier to enter the store. The products they take from the shelves are tracked by cameras and sensors, enabling the customer's card to be charged after they have left the shop.
The shop sells a comparable range of products to other convenience stores such as Tesco Express and Sainsbury's Local. The range includes Amazon own-brand goods as well as products from the Morrisons and Booths supermarket chains.
The shop is open daily 7am to 11pm. Until 20 April, customers get a discount of £10 on their first shop.
There is also a desk where Amazon parcels can be collected and returned.
Similar just-walk-out shops are being trialled elsewhere in London by Sainsbury's, Tesco and Aldi.