Migrate and emigrate

emigrate - leave a place of residence (often a country) for another
migrate - to move from one locality to another

This may also help:
http://www.uhv.edu/ac/student/writing/grammartip021505.htm

Thanks to Julielai's post, I'd say
you emigrate to a place you know
but you
migrate from some place

KhaiMinh,

Migrating (moving residency from one country to another) has two sub-categories :

1. Immigrate : To enter a country of which one is not a native for permanent residence.
2. Emigrate : To leave one's place of residence or country to live elsewhere.

ex: For the last two years I have been thinking about migrating. I want to emigrate from the Philippines

More examples:

US Census Bureau has been tracking migration patterns within the U.S.
INS keeps track of immigrants who come in the United States.
Statistics on emigration from the U.S. is kind of sketchy.

Another use of "migrate" is to describe the annual movement of certain birds and animals from one place to another -- "many birds migrate to warmer locations for the winter."

Is it correct?

I want to emigrate from India and immigrate to US.

In your sentence, usages of "emigrate" and "immigrate" are correct. However, most writers would rearrange the sentence as

I want to emigrate from India to the US.

Thanks Bhae.

Meanwhile, does the word 'the' come before 'US' in your sentence?

I want to emigrate from India to US.

Yes, bvpraveen.
When you refer to America as a country, you must use "the U.S." (the United States - nowadays many would omit the dots though.)

U.S. (without "the") can be used as adjective. Ex: U.S. import, U.S. currency, U.S. dollars.

Is it applicable to all country names or just to US?

Eg. Which are correct?

1) I want to emigrate from US to India?
2) I want to emigrate from THE US to India?
3) I want to emigrate from THE US to THE India?