Simple past usually goes good with things that are completed in the past like I watched a movie yesterday or I went to a party last week. So It takes point of time in the past But when you say I just woke up it doesn't make sense as the action is just completed and the day is still continuing. So present perfect should be used here. I've just woken up is the one to go with.

If you mean that you woke up a few moments ago, both are correct. A speaker of US English is more likely to say the first (past simple), whereas a speaker of GB English would probably say the second (present perfect).