The phrase 'immigrating to' is correct and can be used in written English.
For example: Thousands of people are immigrating to Canada every year in search of a better life.
Donald Trump has suggested a discriminatory immigration policy barring Muslims for immigrating to the US.
And almost none of the people I spoke with seemed interested in immigrating to the U.S.
Celia Dropkin lived in Warsaw and Kiev before immigrating to the United States in 1912.
After immigrating to America from India, Mr Gupta rose quickly in the business world.
(The family, of Russian descent, changed its name after immigrating to the United States in 1939).
His father lived in Turkey in the 1920's before immigrating to the United States.
In his last years, Richard Wagner often spoke of immigrating to America.
Immigrating to the United States at age 15, Zukor entered the penny-arcade business in 1903.
Before immigrating to England, your grandfather was a czarist colonel from a noble Russian family.
After immigrating to America, he opened a medical practice in the Bronx, practicing until his retirement.
What matters isn't that wealthy people are immigrating to Vancouver from China, or anywhere else, really.
