NFL quarterback Tarvaris Jackson will NOT be prosecuted for allegedly pulling a loaded gun on his wife and threatening to shoot her ... TMZ Sports has learned. 33-year-old Jackson was initially charged with aggravated assault with a deadly weapon after he allegedly pointed a loaded gun at his wife…

NFL quarterback Tarvaris Jackson -- who played for the Seahawks last season -- was arrested in Florida after allegedly PULLING A LOADED GUN on his wife and threatening to kill her. TMZ Sports has confirmed ... the 33-year-old was arrested around 2 AM Friday for aggravated assault with a deadly…