Designing a circuit with a bi-colored LED for indicating power vs. system ready
Here's a third way. Does not require that the green LED is powered by GPIO.







simulate this circuit &ndash; Schematic created using CircuitLab

EDIT: I have updated the schematic above, so let's go through the changes in some more detail.


I'm assuming that you are building this and not designing a PCB, so I looked for a through-hole transistor. There were not many good logic-level MOSFETs in TO-92 package, so I went for a BJT.
The 2N3904 recommended by Passerby would work, but I chose a BC547 because it had a nicer datasheet.
The supply was changed from 3.3V to 5V because of the current issues mentioned below. As a result, the resistor values have been increased.
Note that the resistors are different. This is because red LEDs have a lower forward voltage than green LEDs. You may need to tweak these values to get the brightness you desire.