The chain has teamed up with the firm UberEATS to offer the service through its app, offering delivery up to one mile away from participating shops.
The companies have set a £2.50 delivery charge with no minimum spend.
The delivery menu features breakfasts, hot and cold drinks, bakes and sausages rolls, freshly-made sandwiches and sweet treats.
If successful the delivery service could be rolled out to other cities.
Greggs’ chief executive Roger Whiteside said: “This latest innovation will enable customers to enjoy our great-tasting, good-value food wherever they are, offering them the ultimate convenience.”