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 the NHS pay review body and Doctors and Dentists Pay Review Body (DDRB).
This is in contrast to England, where staff will not be given the 1% increase recommended by the NHS pay review body.
Mr Neil said: "e'll deliver on that approach in Scotland's NHS, ensuring our hardworking and dedicated staff rightly receive the wage increases they were promised.
"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 for NHS workers underlines our commitment to frontline staff."
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."
The pay rise means a nurse on the most common payscale, band 5, will see their pay increase to £24,063.