I have decided on + object
I have decided to + verb
The usage is based on the construction of the sentence. You could say:
I have decided to buy a blue carpet for the bedroom.
I have decided on
emigrating [or emigration] to Australia.
As mentioned in John Lawler's comment, there is a subtle difference between the two. Decide to suggests that you have chosen a plan of action.
I have decided to emigrate to Australia.
I might have been considering staying at home, or I might have been considering other countries, but at any rate, this is what I am going to do.
Decide on suggests that you have chosen one from two or more options that you were weighing.
I have decided on emigration. I am going to Australia. (OR – I have
decided to emigrate to Australia.)
I was considering England, Canada and Australia, but I have finally chosen Australia.