The set, which released on June 9, pushed 1,80,000 equivalent album units, including 1,62,000 in traditional album sales, in the week ending June 25, according to Nielsen Music.
The 32-year-old singer previously scored two No. 1 albums on the chart with "Teenage Dream" and "Prism".
"Witness" has become the first album by a woman with the biggest sales week in 2017 since Lady Gaga's "Joanne" last year.
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