The rise will come into effect from 1 April.
NHS staff earning less than £22,000 will also be given a financial top-up to ensure their salary rises by at least £400.
The Scottish government said the increase gave health workers north of the border the highest pay rates in the UK.
The rise comes after Scottish ministers accepted recommendations on pay from the NHS Pay Review Body and Doctors' and Dentists' Pay Review Body.
Health Secretary Shona Robison said the Scottish government was committing almost £100m to ensure all NHS staff groups in Scotland received a 1% pay increase.
She added: "While the independently-recommended uplift is modest, it comes against the background of substantial cuts in Scotland's budget from Westminster and will continue to give NHS staff in Scotland a better deal than their counterparts south of the border.
"As well as delivering the fully-consolidated pay rise for NHS staff, and guaranteeing that all employees are paid at least the living wage, we are also committed to no compulsory redundancies for NHS Scotland staff.
"Our commitment to this pay increase, and to the living wage, for NHS workers underlines the value we place on frontline staff who work incredibly hard every day to care for the people of Scotland."
The Royal College of Nursing (RCN) welcomed confirmation that the Scottish government had accepted the independent pay review recommendations.
RCN Scotland associate director Norman Provan said: "A 1% pay increase does not make up for the below-inflation pay increases which NHS staff in Scotland have received over the last few years, which means their pay has been cut in real terms.
"Restraining pay while the demands on our health services are soaring is a false economy and will do nothing to relieve the difficulties which many health boards are experiencing in trying to recruit nursing staff."
Scottish Labour public services spokeswoman Jackie Baillie said: "NHS staff work incredibly hard and it is right that they are rewarded, but only a third of them believe there are enough staff to do their jobs properly.
"Rather than crowing about what she herself admits is a modest rise, the SNP health minister should focus on why the NHS under the SNP government isn't getting the resources it needs."
Health workers in Scotland are to receive a 1% pay rise for the third year in a row.