The US rapper knocked Sam Smith’s In The Lonely Hour into second place with his third studio album.
To Pimp A Butterfly beat Kendrick’s last chart record, which saw his 2012 UK debut Good Kid M.A.A.D City enter the charts at number 16.
Kendrick’s new album broke Spotify’s streaming record last week, notching up 9.6 million streams on the album’s first full day of release.
To Pimp A Butterfly was also named the most-streamed album in the UK top 40, earning 3,722 streams in a week.
The jazzy album marks a more political direction for the young rapper, with songs about racial injustice and economic inequality in the US.
Elsewhere in the charts, Dire Straits star Mark Knopfler earned the highest-charting album of his career with his eighth studio opus Tracker coming in at Number 3, while Ed Sheeran's X was at 4.
Rounding off the Top 5 was Van Morrison's Duets - Re-working The Catalogue. The singer-songwriter's 35th studio album is his highest-charting collection since 2005's Magic Time, which peaked at 3.
Meanwhile Icelandic composer Olafur Arnalds, who provided the music for ITV series Broadchurch, topped the Official UK Classical Chart for the first time with The Chopin Project.