The posthumous collection of alternative versions of classics, unreleased tracks and covers hit the number one spot after being released last Monday.
Producers Salaam Remi and Mark Ronson put the 12-track album together after listening to thousands of hours of recordings by the singer, who died in July aged 27 following years of drug and alcohol abuse.
The Official Charts Company said the album sold more than 194 000 copies to give Winehouse the biggest weekly sales tally of her career.
'Proud of my daughter'
The record replaces In Case You Didn't Know by British singer-songwriter Olly Murs at the number one spot in the album chart.
Some of the proceeds from the album will go towards the Amy Winehouse Foundation, set up in the singer's memory to help fund charities that support young people.
"It's such amazing news that Amy's album has gone to number one, and just goes to show what she still means to people," said the singer's mother Janis Winehouse.
"It's especially good for the foundation and knowing that every sale will go to help a deserving cause makes the news all the more special. I'm so proud of my daughter and so happy that she is still touching people."
Winehouse was found dead at her London home on July 23. An inquest in October found that she was more than five times over the British drink-drive limit at the time.
Following her death, her second album Back to Black - first released in 2006 - became Britain's highest-selling album of the 21st century, before being toppled by Adele's Grammy-nominated 21 this week.
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