Τελικά έχω φτάσει στο σπίτι.

Here Τελικά means something like finally, eventually, or in the end.

In this sentence, it gives the feeling that getting home took time, effort, or was uncertain, and now the speaker is saying that it has happened at last.

So:

• Τελικά έχω φτάσει στο σπίτι. = Finally, I’ve arrived home.

A useful nuance:

• τελικά can sometimes mean after all or in the end, depending on context.
• Here, finally is the most natural sense.

Greek often drops subject pronouns when they are not needed.

The verb έχω already tells you the subject is I:

• έχω = I have
• έχεις = you have
• έχει = he/she/it has

So Τελικά έχω φτάσει στο σπίτι already clearly means I have arrived home.

If you add εγώ, it usually adds emphasis or contrast:

• Τελικά εγώ έχω φτάσει στο σπίτι.
  = I, at least, have finally gotten home.

So leaving out εγώ is the normal, natural choice.

Έχω φτάσει is the present perfect type of form in Greek, and έφτασα is the simple past (aorist).

Very roughly:

• έχω φτάσει = I have arrived / I’ve made it
• έφτασα = I arrived / I got there

The difference is similar to English, but not identical.

In this sentence

έχω φτάσει focuses on the completed result with relevance now:

• I have arrived, and now I am home.

Important note for learners

Modern Greek often uses the simple past in places where English would use the present perfect.

So in everyday speech, Greeks very often say:

• Τελικά έφτασα στο σπίτι.
• Έφτασα σπίτι.

These can still be translated naturally as I’ve finally made it home in English.

So:

• έχω φτάσει is correct and meaningful.
• έφτασα is also very common, and often more conversational.

φτάσει is the form used after έχω to make the perfect:

• έχω φτάσει = I have arrived
• έχεις φτάσει = you have arrived
• έχει φτάσει = he/she/it has arrived

Notice that φτάσει itself does not change for person here.
The part that changes is έχω / έχεις / έχει / έχουμε / έχετε / έχουν.

It comes from the verb φτάνω = to arrive / to reach.

Useful related forms:

• φτάνω = I arrive / I am arriving
• να φτάσω = that I arrive / to arrive
• έφτασα = I arrived
• έχω φτάσει = I have arrived

So if you are wondering why it is not something like φτάνω or φτάσω, the answer is that Greek uses this special perfect construction with έχω + φτάσει.

Because στο is the normal contraction of:

• σε + το = στο

So:

• στο σπίτι = to/at/in the house/home

This contraction is extremely common and standard.

Other examples:

• σε + τον = στον
• σε + τη(ν) = στη(ν)
• σε + τα = στα

So σε το σπίτι is not the normal form in standard Greek; you should say στο σπίτι.

Because Greek σπίτι can mean both house and home, depending on context.

In this sentence:

• φτάνω στο σπίτι usually means I arrive home or I get back home

Even though the literal words are closer to to the house/home, the natural English translation is often home.

Compare:

• Είμαι στο σπίτι. = I’m at home / I’m in the house
• Γύρισα στο σπίτι. = I went back home
• Έφτασα στο σπίτι. = I arrived home

So the exact English word depends on the situation, not just the dictionary meaning of σπίτι.

After σε (and therefore after στο), Greek normally uses the accusative.

So in full form:

• σε το σπίτι

Here το σπίτι is accusative.

With σπίτι, the form looks the same as the nominative, because it is a neuter noun:

• nominative: το σπίτι
• accusative: το σπίτι

So you do not see a visible change in the noun itself.

You can see the pattern more clearly with other nouns:

• στον φίλο = to the friend
• στη φίλη = to the friend
• στο παιδί = to the child

So yes, σπίτι is functioning as an accusative object of the preposition σε.

Yes, it is natural and correct.

It sounds like:

• the speaker has finally managed to get home,
• and the result matters now.

That said, in casual everyday Greek, people often prefer shorter alternatives such as:

• Τελικά έφτασα στο σπίτι.
• Τελικά έφτασα σπίτι.
• Επιτέλους έφτασα σπίτι.

These may sound a bit more spontaneous in conversation.

So your sentence is absolutely fine, but it is good to know that Greek often chooses the simple past where English might prefer I have arrived.

Yes. Greek word order is fairly flexible, and changing it can slightly change the emphasis.

Your sentence:

• Τελικά έχω φτάσει στο σπίτι.

puts Τελικά first, which is very natural if you want to emphasize finally / in the end.

Other possible orders:

• Έχω τελικά φτάσει στο σπίτι.
• Έχω φτάσει τελικά στο σπίτι.
• Στο σπίτι έχω φτάσει τελικά.
  This last one is more marked and much less neutral.

For a learner, the most neutral and useful version is the original one:

• Τελικά έχω φτάσει στο σπίτι.

Usually, with φτάνω, Greek commonly uses σε / στο before a place:

• φτάνω στο σπίτι
• φτάνω στο αεροδρόμιο
• φτάνω στη δουλειά

However, in everyday speech, you will also hear σπίτι without the article in some expressions, especially with verbs of going or returning:

• πάω σπίτι = I’m going home
• γυρίζω σπίτι = I’m going home / back home
• έφτασα σπίτι = I got home

So with σπίτι, omission is possible in casual speech, especially when the meaning is simply home.

Still, for a clear, standard learner version, στο σπίτι is completely safe and very common.