Travellers attempting to buy tickets using the old app were prompted to visit the app store on their Apple or Android device to download the new version.
It is an entirely new app - not an update - and requires a new password and payment details to be added.
Before logging in, passengers also needed a password reset email, but many reported long delays before this appeared in inboxes.
For travellers who were eventually able to log in, their journeys simply did not appear when they attempted to search for trains.
The ScotRail website booking system also failed to show available trains.
ScotRail said in a statement: "We're sorry for the delay to anyone switching their ScotRail app today.
"We are working with our technical teams to clear this as quickly as possible and we apologise for the inconvenience."
