The monument, at Waterloo Station, pays tribute to the thousands of people who arrived in the UK from Caribbean countries between 1948 and 1971.
It depicts a man, woman and child standing on top of suitcases and was revealed to mark Windrush Day.
The government gave £1m to fund the statue, designed by Basil Watson.
In a message to mark the occasion, signed Elizabeth R, the Queen said she hoped the statue would “inspire present and future generations” as she sent her “warmest good wishes on this historic occasion”.
Windrush Day marks the arrival of Caribbean immigrants to the shores of Britain on 22 June each year – the day HMT Empire Windrush arrived at Tilbury Docks in 1948.
The Queen’s grandson the Duke of Cambridge helped to unveil the statue, alongside his wife the Duchess of Cambridge, and also paid tribute to the contributions of the Windrush generation, and their descendants to British life.
“Without you all Britain would simply not be what it is today,” he said. “I want to say a profound thank you to every member of that generation and the generations that have followed.”
But Prince William also talked about how the “past weighs heavily” on the people of the Caribbean and the Windrush generation.
He said members of the Windrush generation had been victims of racism when they arrived and said “discrimination remains an all too familiar experience for black men and women in Britain in 2022”.
The duke referred to the Windrush scandal, which broke in April 2018, and said it still “rightly reverberates through the Caribbean community here in the UK”.
The scandal, which saw members of the Windrush generation and their children wrongly detained and even deported, led to the UK government apologising for the deportation threats many faced.