VS Code starts debugging in integrated terminal instead of debug console

Edit 3

As with the release 2019.4.0 of the python extension it is now possible to set the console option to internalConsole (#4321).

In .vscode/launch.json:

"console": "internalConsole"

Edit 2

As suggested in omartin2010’s answer you can additionally set the option

"internalConsoleOptions": "openOnSessionStart"

to automatically open the debug console when starting debugging.

Edit 1

Setting the “console” option explicitly to "none" was originally the way to go (see answers), but now “none” is no longer valid (see Edit 3 above)

"console": "none"

Original answer

To ensure that the output is written to the debug console you can set the debugOptions.
Adding the following entry to your configuration in yourlaunch.json should fix it:

"debugOptions": [
    "RedirectOutput"
]