Washington Football Team QB Alex Smith made his official return to full practice on Tuesday ... nearly 2 years after he ALMOST DIED from complications following a devastating leg injury.

You can see in the amazing footage ... Smith runs through drills alongside QB Dwayne Haskins -- even connecting on a short pass to running back Antonio Gibson.

This is IMPROBABLE video considering everything Smith has gone through over the past 2 years.

Remember, the QB suffered a compound fracture in his right leg -- the bone broke through the skin -- during a game in November 2018.

Days later during his recovery, Smith became VERY sick and his leg turned black. He was diagnosed with sepsis -- a life-threatening condition that stems from a bad infection.

Doctors later determined Smith had a flesh-eating bacteria that ultimately required 17 surgeries!!!

Somehow, Smith battled through all of the procedures, all of the rehab ... all of the mental torture -- and was CLEARED by docs to return to the field over the weekend.

Alex's family celebrated the news with a champagne-spraying party -- and cake! Amazing moment.

And, now, once again Smith is beating the odds ... most everyone though the 36-year-old would just hang up his cleats and move on with his life.

But, Alex made it clear football is his passion and made it his mission to get back on the field.

Mission accomplished.