Så fort paketet kommer, ringer jag dig.

Here så fort means as soon as.

So:

• Så fort paketet kommer = As soon as the package arrives

It does not mean so fast in this sentence, even though fort often means fast/quickly in other contexts.

Compare:

• Han springer fort. = He runs fast.
• Så fort jag hinner, hjälper jag dig. = As soon as I have time, I’ll help you.

Så snabbt usually refers more directly to speed, not to time clauses like as soon as.

Paketet is the definite form of paket.

• ett paket = a package
• paketet = the package

In Swedish, definiteness is often shown by adding an ending to the noun, rather than using a separate word like the.

So:

• Så fort ett paket kommer ... = As soon as a package arrives ...
• Så fort paketet kommer ... = As soon as the package arrives ...

Swedish very often uses the present tense to talk about the future when the time is clear from the context.

In this sentence:

• kommer literally looks like comes
• ringer literally looks like call/am calling

But together with så fort and the situation, the meaning is future:

• As soon as the package arrives, I’ll call you.

This is completely normal in Swedish.

You could think of it as similar to English in sentences like:

• When he arrives, I’ll call you.

English also often uses present tense in the time clause (when he arrives, not when he will arrive).

Kommer can be confusing because it appears in more than one structure.

Here, kommer is simply the present tense of komma:

• paketet kommer = the package arrives / comes

But Swedish also has a future-like construction:

• jag kommer att ringa = I will call

That is a different pattern:

• kommer att + infinitive

In your sentence, there is no att + infinitive, so kommer just means arrives/comes.

This is because Swedish has V2 word order in main clauses: the finite verb usually comes in the second position.

The sentence starts with a subordinate clause:

• Så fort paketet kommer, ...

After that, the main clause follows, and the finite verb must come before the subject:

• ringer jag dig

So the full structure is:

• Så fort paketet kommer, ringer jag dig.

If you started with the main clause instead, you would get normal subject-verb order:

• Jag ringer dig så fort paketet kommer.

Both are correct.

The comma separates the subordinate clause from the main clause:

• Så fort paketet kommer, = subordinate clause
• ringer jag dig. = main clause

In Swedish, commas around subordinate clauses are not always used exactly the same way as in English, and usage can vary somewhat by style. In a sentence like this, the comma is very common and helps readability.

So the comma is mainly marking the boundary between:

• the time clause
• the main statement

Dig is the object form of du.

• du = you (subject)
• dig = you (object)

So:

• Jag ringer dig. = I call you / I’ll call you.

Compare:

• Du ringer mig. = You call me.
• Jag ringer dig. = I call you.

English uses you for both subject and object, but Swedish changes the form.

Yes. Så snart can also mean as soon as.

So these are both natural:

• Så fort paketet kommer, ringer jag dig.
• Så snart paketet kommer, ringer jag dig.

In many contexts they are interchangeable. Så fort is very common in everyday speech.

Just remember that fort can also mean quickly, so learners sometimes find så snart a little more transparent at first, because it clearly points to time.

Yes, it is completely natural.

A very common alternative is:

• Jag ringer dig så fort paketet kommer.

That version may feel a little more straightforward to learners because it keeps the main clause first.

Both mean the same thing:

• Så fort paketet kommer, ringer jag dig.
• Jag ringer dig så fort paketet kommer.

The first version puts more focus on the time condition: as soon as the package arrives.

In casual speech, this sentence is already quite natural. A speaker might also say:

• Jag ringer dig så fort paketet kommer.

That may be slightly more common in everyday conversation simply because many speakers prefer main clause first.

Pronunciation-wise, in fast speech:

• ringer may sound a bit like ringer with a light ng
• paketet is often pronounced smoothly, with the stress on the first syllable: PA-ke-tet

But grammatically, the written sentence you have is standard and idiomatic.