The programme is part of Royal Mail Group's strategy to grow its express parcels business in the UK and worldwide.
The Royal Mail said the "vast majority" of jobs would be full-time, representing a near-20% increase in its 5,300 workforce, with most roles related to delivering and collecting packages.
Moya Greene, Royal Mail chief executive, said: "Our £75m investment is part of Royal Mail Group's strategy to grow its parcels businesses in the UK and overseas.
"Our strategy is to convert the rise in parcel volumes in to profitable growth. That means becoming a much more customer-focused company being run on commercial lines and investing in new, vital technology," she added.
Mark Hoban, Minister for Employment, said: "It is great news that 1,000 new jobs will be created across the country as a result of this investment.
"We've now got a record number of people in employment and these jobs will provide welcome opportunities for people who are looking for work."
Dave Ward, deputy general secretary of The Communication Workers Union (CWU), claims 10 times more workers have left the Royal Mail over the past two years than will be taken on by parcelforce.
Ward said: "These jobs will go some way to easing the impact of jobs lost elsewhere in the company as huge changes are brought in to address the altering profile of mail."
