The 14 songs are drawn from throughout his career, which spanned from the early 1950s to his death in 1977 aged 42.
Priscilla Presley said the album gave his songs the sort of huge backing he always wanted in studio recordings but only got during his 1970s Las Vegas concerts.
"This is an album that Elvis always really wanted to do and he would have been so pleased to know his fans are still there and they continue to love his music," she said.
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The recording shifted 79,000 copies in its first week on release, taking it to number one.
Presley first topped the British album charts this week 59 years ago with Elvis Presley Rock n' Roll.
He is now the first solo artist to ever have a UK number one album in five different decades.
It is his third UK number one album since his death, all three coming since 2002.
-AAP