This is something that I have never done before. It might seem trivial but I'm an overthinker. I heard about this gathering my friends are having and one of them said I should come.
So I asked the same friend if the host would be cool with it, and he said that the host wants me to come.
How do I tell the host that I am indeed coming to the party?
Ask the host what you should bring along
This clearly carries the message that you will bring the item you will bring. And this clearly shows that you will be coming to bring the item you have offered to bring.
Don't show up empty-handed. Ask the host "what do you need?" and bring that.
Something token like a bag of chips/crisps, or if you cook make something like scones or biscuits/cookies.
If the host says "don't bring anything" then you can either listen or show up with a bottle of wine or soft-drink or juice, because that's always useful.
Either way, you had a conversation with the host and they now know you're coming.
Expansion, I personally do this with my sister, she used to say "just bring yourself", until the day I said "tell me what you need or I'll bring Haggis" so I turned up with canned Haggis. Since that time, she now says what they need.
Either way, she now absolutely knows we're intending on coming. This is my personal experience, in western society.
I like Criggie's answer but would like to propose a slightly different approach in such a case. Without the person throwing the party specifically inviting me first, I would first approach this person to confirm, and then only do what Criggie suggests and ask what I can bring. Something around the lines of:
Hey! X told me I could join the party you're throwing on xxxx and I just want to confirm that with you. If yes, can I bring something like dessert or a bottle of wine?
I would be doing this in any case, and even more in the current sanitary situation. Where I live there's been some restrictions around the number or people who can gather and X might not care while the person throwing the party might. Even without a legal restriction, people nowadays may want to throw smaller parties, not inviting at once everybody they may have invited before this crisis.
