Britain would be poorer without the efforts of the Windrush generation, Prince William said as he and Kate attended the unveiling of a memorial at London's Waterloo Station.
The 12-foot statue - of a man, woman, and child in their Sunday best standing on top of suitcases - was unveiled on Wednesday to mark Windrush Day.
It is one of dozens of events and activities happening across England.
Next year, it will be 75 years since the HMT Empire Windrush arrived at Tilbury docks in 1948, bringing 500 passengers from the Caribbean.
The government, which has provided £1m in funding for the monument, said it "symbolises the courage, commitment, and resilience of the thousands of men, women, and children who travelled to the UK to start new lives from 1948 to 1971".
It also acknowledges the Windrush generation's "outstanding contribution" to British society and is intended to be a "permanent place of reflection".
The Queen sent her congratulations on what she called a "historic occasion".
Prince William said discrimination "remains an all too familiar experience for black men and women in Britain in 2022".
The duke added: "Only a matter of years ago, tens of thousands of (the Windrush) generation were profoundly wronged by the Windrush scandal."
It emerged in 2017 that hundreds of Commonwealth citizens had been wrongly detained, deported and denied legal rights, despite having the right to live in Britain.
William said the scandal "rightly reverberates throughout the Caribbean community here in the UK, as well as many in the Caribbean nations".
He continued: "Diversity is what makes us strong, and it is what reflects the modern, outward-looking values that are so important to our country."
The Queen wrote in a message: "The unveiling at Waterloo Station on Windrush Day serves as a fitting thank you to the Windrush pioneers and their descendants, in recognition of the profound contribution they have made to the United Kingdom over the decades.
"It is my hope that the memorial will serve to inspire present and future generations, and I send you my warmest good wishes on this historic occasion."
The memorial was created by Jamaican artist Basil Watson, who said it pays tribute to the "dreams and aspirations, courage and dignity, skills and talents" of the Windrush generation.
He added: "My parents, along with a great many others, took the long, arduous voyage from the Caribbean with very little or nothing other than their aspirations, their courage, and a promise of opportunity for advancement.
"This monument tells that story of hope, determination, a strong belief in selves and a vision for the future."