Jesse had small roles in "Something About Mary" and "Hall Pass," big-screen comedies his dad wrote, directed and produced with his brother Peter, Jesse's uncle.
"It is with profound sorrow that we accept the passing of our beloved Jesse following his struggle with addiction. We fully trust that he is now in the hands of our Lord," the Farrelly family said in a statement Friday.
"We are immeasurably grateful for the abundance of happiness and laughter he brought into our lives, and we will rejoice eternally for all the moments we got to breathe in his wondrous spirit. The family thanks you for your well-wishes and kindly asks that you respect our privacy during this difficult time."
TMZ said Jesse Farrelly died Wednesday night of an apparent drug overdose.
An autopsy conducted Thursday proved inconclusive and officials are awaiting the results of toxicology tests before determining the cause of his death.