Jeff Sperbeck, John Elway‘s longtime agent and friend, is being remembered by his family after his death … they say he was a wonderful man.

Jeff’s wife, Cori, and the Sperbeck family tell TMZ … “We are deeply saddened to share the passing of our beloved Jeff Sperbeck. He was a wonderful father, husband, brother, son and friend to many and will be profoundly missed by all.”

The family adds … “We are grieving this unimaginable loss as a family alongside our dearest friends the Elways and the many other clients Jeff called friends. We are grateful for the overwhelming  outpouring of support that we have received and ask for privacy for our family at this difficult time.”

TMZ Sports broke the story … John and Jeff, along with several of their family members, were leaving a post-Stagecoach party on Saturday around 7 PM when Sperbeck fell off of a golf cart that was driven by the Hall of Fame quarterback.

Jeff smacked his head on the ground, suffering a traumatic brain injury.

Elway called 911 … but despite the medics and doctors’ best efforts, Jeff’s life could not be saved.

Doctors kept Sperbeck on life support until his organs could be harvested for donation … and he was officially pronounced dead Wednesday morning at 1:10 AM.

Elway also released a statement after Jeff’s death, saying … “I am absolutely devastated and heartbroken by the passing of my close friend, business partner and agent Jeff Sperbeck. There are no words to truly express the profound sadness I feel with the sudden loss of someone who has meant so much to me.”

John added … “My heart and deepest sympathies go out to Jeff’s wife, Cori; his children Carly, Sam and Jackson; and everyone who knew and loved him. Jeff will be deeply missed for the loyalty, wisdom, friendship and love he brought into my life and the lives of so many others.”