Both sides agreed on Sunday to a deal brokered by mediators.
“The most important thing – we have now avoided a strike,” representatives for both sides told journalists on Sunday.
“A sound agreement which falls within budget,” according to the Swedish Association of Local Authorities and Regions (SKL).
The new agreement extends over 37 months and can’t be revoked. The agreement was welcomed as having given “peace and calm in the public sector for an extended period of time”.
The dispute related to the size of salary increases, and whether they should be calculated in percent or in kronor terms.
The difference amounted to around a few hundred kronor per month. Unions also sought to remove so-called split shifts involving several hours of involuntary down time.
Nearly 9,000 employees in 100 municipalities had given notice to go on a strike which was due to begin on Monday.
Strike action would have had a major impact in several areas of public services such as hospitals and children’s daycares.
Parents in Stockholm and Norrköping, among other areas, had for example been warned to be prepared for sending their children to school with packed lunches.