The increase takes effect from April and includes extra money for staff earning under £21,000 to ensure their pay goes up by £300.
Health Secretary Alex Neil said it means nurses will get a better deal than south of the border.
The changes follow recommendations from NHS pay review body and Doctors and Dentists Pay Review Body (DDRB).
Mr Neil said he would not follow the path taken by his Westminster counterpart, Jeremy Hunt.
"Today, I can confirm we'll deliver on that approach in Scotland's NHS, ensuring our hardworking and dedicated staff rightly receive the wage increases they were promised," Mr Neil said.
"This means that all NHS staff groups in Scotland covered by the remits of these bodies will receive a 1% pay increase, and we will supplement the pay of those currently earning under £21,000 to ensure they receive a total increase of £300.
"I have also taken steps to ensure that no NHS Scotland worker can be paid below the Scottish living wage.
"Our commitment to this pay increase, and to the living wage, for NHS workers underlines our commitment to frontline staff delivering services for the people of Scotland."
Tom Waterson, chairman of Unison's Scottish health committee, said: "We are delighted the Scottish Government has decided to implement the recommendations of the pay review body in full.
"We would urge the UK Government to also commit to paying health service staff the recommendations in full.
"We went into these negotiations in good faith and we expect the clear recommendations of the pay review body to be delivered.
"It is good news for NHS staff that the Scottish Government have committed to doing that."
The pay rise means a nurse on the most common payscale, band 5, will see their pay increase to £24,063 by October, when incremental pay is also factored in.
A nurse on the same grade in England will be on £23,825 by the same time, the Scottish Government said.
Dr Brian Keighley, chairman of the British Medical Association in Scotland, said: "We are pleased that the Scottish Government has taken a different approach to that of the Westminster Government to deliver a fairer pay award for NHS staff in Scotland.
"We acknowledge this as a positive first step towards recognising the hard work and commitment of NHS staff in Scotland and addressing the well understood challenges of recruitment and retention of medical posts.
"However this uplift, which the Cabinet Secretary himself describes as 'modest', is yet another year of below inflation pay awards for doctors and other NHS staff who are fundamental to driving NHS service change and are continuing to deliver high quality care to patient despite intense and increasing workload pressures."