Is there a word for a person who believes all events - past, present and future - have all been predetermined?

Solution 1:

A fatalist or a predestinarian.

predestinarian: A person who believes in predestination; a fatalist. Also in extended use. [OED]

From a philosophical standpoint:

In philosophy, a fatalist is someone who holds specific beliefs about life, destiny, and the future. Fatalists share the certainty that fate has already been laid out in front of them, and that they have no real control over what will happen.

vocabulary.com

You can also check:

  • Difference between ‘determinism’ and ‘fatalism’ - philosophy.stackexchange.com
  • Determinism vs. fatalism vs. predeterminism - Wikipedia

Solution 2:

A Calvinist:

Calvinism (also called the Reformed tradition, Reformed Christianity or the Reformed faith) is a major branch of Protestantism that follows the theological tradition and forms of Christian practice of John Calvin and other Reformation-era theologians.

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Predestination:
Reformed theologians teach that sin so affects human nature that they are unable even to exercise faith in Christ by their own will. While people are said to retain will, in that they willfully sin, they are unable to not sin because of the corruption of their nature due to original sin. To remedy this, Reformed Christians believe that God predestined some people to be saved. This choice by God to save some is held to be unconditional and not based on any characteristic or action on the part of the person chosen.