Configure IntelliJ to print the standard output in the console window but also save it to file
This feature is available starting from IntelliJ IDEA 11:
This feature does work in IDEA 14.1.1. Also in Run/Debug configuration.
The writing occurs after the run finishes.
In IntelliJ IDEA 2021.2 this no longer works.
P.S. If your motivation is because you can't scroll back to the output start you can increase how many lines you can scroll backwards.
Screenshot of scrollback buffer size setting.