Je suis réveillé(e).
* Je suis means "I am"
* réveillé(e) means "awake" - use réveillé for a male speaker and réveillée for a female speaker.
Here are some other ways to say it, depending on the context:
* Je suis debout. (I'm up)
* Je ne dors pas. (I'm not sleeping)
* J'ai les yeux ouverts. (My eyes are open)
You can also use the informal "J'suis réveillé(e)" if you're talking to friends or family.