migrate (of birds, animals, and people) = move from one place to another (to live there).

• How do birds know when to migrate and how do their way back home?
• A lot of new software engineers migrated to America where they could earn more.

emigrate (ONLY for people) = leave your own country and make your home in another one.

• Tomy Methipara decided to emigrate to the US.
• Many people emigrate to European countries in search of better prospects.

immigrate (seldom used) = enter a foreign country and make your home there

• He is planning to immigrate to the US next year. (rarely used)
• He is planning to emigrate to the US next year. (commonly used)
• He emigrated from India to the US (here the focus is on India)
• He immigrated to the US from India (here the focus is on the US)

However, the words immigrant and immigration are commonly used.

• Due to the scarcity of jobs, the immigration to Gulf countries has decreased.
• The number of new immigrants to Gulf countries has suddenly decreased.