A Met Office yellow weather warning had been in place across North East Scotland since 12pm on Thursday but was lifted on Sunday.
Speed restrictions put in place across the region as a safety precaution were also removed across most of the network.
Live updates will be available on the ScotRail website, mobile app, and social media channels.
David Simpson, ScotRail Service Delivery Director, said: “The vast majority of services will operate as normal on Monday, and we look forward to welcoming passengers to take advantage of our off-peak all day trial.
“Our first priority is always the safety of customers and staff, and we only run services when we are absolutely sure the lines are safe.
“We thank customers, especially those in the north of the country, for their understanding and patience following the extreme weather. Customers are advised to check before travelling by visiting the ScotRail website, app, or social media channels.”