CAIRO—Egypt's amended constitution, set to be presented to the president on Tuesday, would scale back the influence of Islamic law, enshrine the privileged status of the military and do little to check the resurgent power of police.

The major changes in the document appear intended to prevent another Islamist surge in politics and to grant the military and security forces powers to temper civilian rule. Experts said it essentially reverts back to the old order, adding some updated language with vague assurances on political...