officially would have "died" when the flood ambushed him and Keyes in the 343 Guilty Spark level, rather than when Halo broke apart with him having a cuddle with the elite.
However Sarge didnt die due to him having a disease called Boren's Syndrome, which is the result of being subjected to high yield plasma such as from a Plasma Grenade.
Boren's Syndrome is characterized by migranes, amnesia and brain tumors. If left untreated it is also fatal. It also disrupts the electrical signals in a persons nervous system. Due to the Sarge being a right hard bastard, he refused the 30 weeks of chemotherapy treatment so that he could be back killing Covenant ASAP.
Due to his jumbled nervous system, the flood infection forms were unable to infect Sgt. Johnson and thus rejected him as a host. However due to this attempt at infection he has Flood DNA in his blood, which are very much dead and non-infectious but some gene fragments are intact. It has also given himsome regenerative abilities yet that is not confirmed by Dr Halsey (the Spartans were her creation).
Either way, Sarge manages to get out of the facilty alive and eventually off Halo on a Pelican with a few others and is re-united with Master Chief in orbit of Threshold (the planet that Halo in beside, and if you are clever enough you may be able to jump to a specific, major conclusion just by that sentance).