Official Canon Edit
Fulgrim had been found on Chemos, a mercantile world that had been suffering from closed trade routes. Unlike his brothers who grew up as warriors or leaders, he grew up as a laborer and restored the planet's infrastructure. When the Emperor arrived, Fulgrim swore fealty and recieved the Emperor's Children legion, but due to a gene-seed defect it was undermanned, so he spent an extended amount of time with Horus' legion.
Fulgrim got along quite well with his brothers. He was close to Ferrus Manus and Horus, and Fulgrim was one of the only people who could speak to Konrad Curze. Ferrus and Fulgrim engaged in a friendly competition to create the best weapon, after which they found that they equally good craftsmen, and exchanged weapons.
Fulgrim's relentless pursuit of perfection took an unhealthy turn, when it became a goal in and of itself. Legionnaires took to performance-enhancing drugs and body modifications, including the use of Xenos biology. This obsession attracted Slaanesh, who set eyes upon the fair Fulgrim and sought to claim him as its champion.
Horus Heresy Edit
When Horus revealed his intent to betray the Emperor, Fulgrim unsuccessfully trued to dissuade him, and instead joined his cause. As he became more corrupted, though, he became a less dependable ally, seeking only to indulge himself while his captains had to take over managing his legion.
During the Drop Site Massacre, Fulgrim personally decapitated his brother Ferrus Manus, and after the Heresy, slit Roboute Guilliman's throat. Because Fulgrim regretted not being able to turn Ferrus, he had Fabius Bile clone him repeatedly to try again, and each time he failed.
However, the Daemon Primarch may not be Fulgrim at all, but a daemon inhabiting his sword that has taken possession of his body. Fulgrim allowed the possession due to the guilt he felt over killing Ferrus. The real Fulgrim is possibly still trapped inside a painting, unable to escape free. The real Fulgrim claims to be back in control, but nobody can really say for sure.
TTS Canon Edit
The Emperor claimed that Fulgrim was secretly obsessed with having more fabulous hair than himself, a feat which to this day he has not yet succeeded (despite having lost most of his hair in the last ten millennia).