Alfie Reedman, 20, of Westergate Close, Ferring, walked into Tesco Express in Goring Way on Saturday, 21 October at about 7.50am.
He threatened staff at knifepoint and demanded cash from the till, where he stole hundreds of pounds.
A day later, on Sunday, 22 October, Reedman demanded cash from the till at both The Welcome Store in Half Moon Lane, Salvington and Salvington Food Centre in Salvington Road, Worthing.
He left both stores with nothing and was arrested by officers on Franklin Road.
Reedman pleaded guilty to robbery and two counts of attempted robbery at Brighton Magistrates’ Court on Tuesday, 21 November and was remanded in custody.
He is due to appear at a court to be fixed on Tuesday, 16 January 2024 for sentencing.
Detective Inspector Gary Jacobs said: “This incident caused huge amounts of distress to shop workers and it is not something anyone should have to experience when going to work.
“Reedman’s unnecessary actions that weekend will be punished, and I hope the court gives him a worthy punishment in January to stop him from doing this again.”