Karl Urban's action movie, based on the cult 2000AD comic book character, pulls in £1 million to become the first 18-rated film to emerge as UK box office champ since Saw 3D in 2010.
Dredd sees off competition from Tom Hardy's Lawless and the Keira Knightley-led Anna Karenina adaptation to secure first place.
Last week's number one movie Total Recall saw a sharp 73% decline in ticket sales as it drops to number four. Brave, Pixar's animated tale of a princess in the Scottish Highlands, is at number five in its sixth weekend on release.
Elsewhere, comedy movie The Watch experiences a huge 85% dip in box office takings to tumble down seven places from last week's number two slot.
The UK box office top ten in full:
1. (-) Dredd - £1,049,345
2. (-) Lawless - £973,234
3. (-) Anna Karenina - £875,702
4. (1) Total Recall - £675,280
5. (3) Brave - £649,057
6. (5) The Possession - £533,334
7. (4) Ted - £479,943
8. (6) The Dark Knight Rises - £352,587
9. (2) The Watch - £338,184
10. (7) The Bourne Legacy - £270,180
Watch Digital Spy interview Dredd star Karl Urban below: