Sometimes when I come back from my brother's house he asks me to let him know when I am at home. Now, in that situation which one of the following is correct :
I've reached home now.
I've arrived home now.
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Notice that 'reach' is strictly divalent: you can't say "I've just reached." You must add a noun group or a locative:
"I've just reached the station."
"I've just reached home."
"We've only just reached here."
'Arrive' is intransitive
"We've just arrived (/ at the station)."
The fact that it also can be followed by a locative confuses the issue:
"I've just arrived home / here."
I suspect it depends on the actor. If you are going towards a place then you can say that you are 'arriving'. On the other hand, for someone who is sitting at that place, you are reaching that place.
I am reaching the railway station sounds OK for me to say; but for people who are already at the railway station
one more passenger is arriving.
So I would prefer
PS: I am not a native speaker.
In this case, "I've arrived home" sounds more natural.
The difference is subtle. "Reached" can suggest a stage in a long or difficult journey, while "arrived" may give more of a sense of a journey's end. "I've arrived home" sounds like the end of the story. "I've reached home" suggests than you may keep going, or that getting there was a difficult accomplishment.
The origins of the words give a hint of the flavour. To reach means to stretch out, while arrive means to come to the shore (ending a journey by ship).