The Jedi Master who ordered the formation of the clone army was Sifo-Dyas.
Sifo-Dyas was a Jedi Master and member of the Jedi High Council who foresaw that the Galactic Republic would eventually face a major war. Acting secretly, he commissioned the Kaminoans to create a clone army for the Republic. His decision was made without the broader Jedi Order's approval.
Before the events of Attack of the Clones, Sifo-Dyas was killed under orders connected to Count Dooku and Darth Sidious. Dooku then took control of the clone-army project, hiding its true political purpose and ensuring that the army would eventually serve the Sith's plan. The Kaminoans continued to believe they were fulfilling a legitimate Jedi request.
Obi-Wan Kenobi discovers the army on Kamino while investigating the assassination attempt against Senator Padmé Amidala. The Jedi initially assume the clones were created for the Republic, but the later revelation of Order 66 shows how the project was manipulated. Sifo-Dyas ordered the army's creation, but he did not design the Sith conspiracy behind it.