John Elway's Son -- GUILTY in Domestic Violence Case

John Elway's son -- a former Arizona State University quarterback -- has been sentenced to domestic violence counseling after an altercation with his GF back in July ... TMZ Sports has learned.

As we previously reported, the 25-year-old was arrested in Denver back in May after getting into an argument with his girlfriend and allegedly dragging her out of his car by her hair.

According to the police report, Elway then pushed her down to the ground as she tried to get up.

Elway was initially charged with assault and disturbing the peace -- but struck a plea deal with prosecutors in which he agreed to plead guilty to the D.T.P. and in exchange the assault charge was dismissed.

In the end, Elway was sentenced to 1 year probation -- with "monitored sobriety" -- he was ordered to pay fines, can't own firearms and may not have any contact with the victim.