The privatised postal group said parcels will be delivered on Sundays later in the summer to addresses within the M25 motorway, including London.
Around 100 delivery offices across the UK with the highest parcels volumes will be open on Sunday afternoons as part of the initiative.
Royal Mail’s delivery offices are currently open six days a week.
The firm’s express parcels business, Parcelforce Worldwide, will also launch a Sunday delivery service in June for online shoppers through participating e-retailers.
Parcelforce Worldwide will make the service available to contract customers across the UK.
Shoppers who choose the Sunday service through registered retailers will receive a text message between 30 and 90 minutes before delivery.
Royal Mail said the moves were being planned under the Agenda for Growth agreement with the Communication Workers Union (CWU).
Chief executive Moya Greene said: “Through these new Sunday services we are exploring ways to improve our flexibility and provide more options for people to receive items they have ordered online.
“The support of the CWU has enabled us to respond quickly to a changing market.”
CWU deputy general secretary Dave Ward said: “Royal Mail’s announcement about expanding delivery and collection services to seven days a week is an exciting innovation which we welcome.”
“We have worked closely with Royal Mail to develop how best we can go forward to grow the company together and improve the services for customers.
“We appreciate that in order to stay competitive in a broadly unregulated sector Royal Mail has to expand its services to its customers. We believe that offering Sunday delivery and collection services is the right response from the company.
“With ever-increasing numbers of people opting to shop online, Sunday services are necessary to deal with the growing demand in parcel delivery.
“Earlier this year we delivered a groundbreaking deal for Royal Mail workers and we are committed to continuing to set the benchmark for terms and conditions across the postal industry.
“The union is negotiating with Royal Mail nationally to ensure that postal workers who are affected by these changes receive good terms and conditions and where appropriate, that work is performed on a voluntary basis.”