“Decide to” is followed by the infinitive.
“Decide on” is followed by a verb in the –ing form or a noun / noun phrase.

You decide to do something.
But you decide on doing something, or you decide on something.

“Decide to” is stronger and more definite than “decide on”.
“Decide to” states that a decision has been made and states what that decision was.
“Decide on” may only state that a decision has been made. What that decision was may be implied, but it may not always be clear.

Consider the following examples:

Decide to plus infinitive
“We have decided to purchase our company’s competitor in Florida.”
“Great! When’s the transaction going to be closed?”

Decide on plus –ing
“We have decided on purchasing our company’s competitor in Florida.”
“Yeah? So you’re actually going to buy it?”

Decide on plus noun phrase
“We have decided on the purchase of our company’s competitor in Florida.”
“So what have you decided?”

These examples show the gradation of meaning of the three different structures. With “decide to”, the meaning is clear. “Decide on plus –ing” is similar, but may be ambiguous in certain circumstances. “Decide on plus noun / noun phrase” is not clear.

If you make a decision on something, we only know for certain that a decision has been made. It may not be clear whether the decision was positive or negative.

Make a decision on plus noun phrase
“We have made a decision on the purchase of our company’s competitor in Florida.”
“So what have you decided?”

Using the –ing form does not make the sentence much clearer.

Make a decision on plus –ing
“We have made a decision on purchasing our company’s competitor in Florida.”
“That sounds positive, but what have you decided?”

However, if you use “to” plus infinitive instead of “on”, the meaning is clear.

Make a decision to
“We have made a decision to purchase our company’s competitor in Florida.”
“Great! When’s the transaction going to be closed?”

More examples:

“We have made a decision to sell the company.”
“Really? When are you going to tell the employees?”

“We have made a decision on the sale of the company.”
“So, what did you decide?”

“During the meeting we decided to take on more staff.”
“Great – but is the office big enough?”

“During the meeting a decision on taking on more staff was made.”
“So what was the decision?”

Note on “make a decision”: Many style guides discourage writers from using this phrase. The noun “decision” is a nominalisation of the verb “decide”. It is shorter and – as you can see – often clearer, to simply use the verb.

“Decide on” is also a phrasal verb. It means “to choose something or someone after careful thought”. It is usually followed by a noun / noun phrase. In the examples below we know that a decision was made and also what that decision was.

After several months of looking for premises we’ve finally decided on a warehouse on the motorway outside Manchester.

It was very difficult to choose between Mark and Julia for the position of Head of HR, but we finally decided on Julia.

After consulting an interior designer, we decided on wood panelling for the meeting room.