The pay rise will be backdated to April 1, having been recommended by the NHS Pay Review Body.
This award represents an estimated increase of approximately £88.24 million on the Agenda for Change pay bill.
Health Minister Mr Swann said: “I want to once again place on record my gratitude and admiration to all who work in our health and social care system.
“So many staff have worked extremely long hours under enormous pressure during the pandemic.
“Staff are the backbone of our health and social care services and I want to recognise their continued professionalism in delivering high-quality effective care to people across Northern Ireland. ”
Mr Swann said the increase would ensure that “pay parity with England is maintained”.
He said he wanted to see the pay increase and the payment of associated backpay “progressed as quickly as possible”.
Mr Swann also acknowledged calls from unions for enhancements to the pay award for 2021 and 2022.
The department and trade unions have been in discussions in recent weeks about possible enhancements to the pay award for 2021/22.
He said: “Any additional non-consolidated award will need to be approved by the Department of Finance.
“Like all my Executive colleagues, I have to operate within budgetary constraints set by the Treasury.
“While there are many conflicting demands on health spending, I am clear that properly rewarding staff is an important priority.”
The 3% pay increase will be made in addition to the HSC special recognition payment which was announced early in the year.
This one-off payment of up to £735 acknowledged the efforts made by staff across the HSC workforce during the pandemic.