Johnson was a part of the SPARTAN-I project, originally called the ORION project. The Master Chief was a SPARTAN-II, the best of the best.

Is Sergeant Major Johnson a Spartan?

He was a spartan-1. He was appearently in the ORION project, a project that created super-soldiers. Except that these spartans didn't get special armor.

Who were the Spartan 1s?

SPARTAN-1.1

The children of the SPARTAN-Is are sometimes referred to as Spartan 1.1s. There are sixteen Spartan 1.1s, including Janissary James and Kevin Morales. Due to their parents' augmentations, the Spartan 1.1s had to receive injections in order to ensure normal growth without defects.