The Browns moved for Bess in April in a trade with the Miami Dolphins, which saw the teams exchange their positions in the fourth and seventh rounds of the 2013 draft.
Chudzinski told reporters: "Going back with Davone, what a great pickup for us and I couldn't be more pleased with what he's done both on the field and off the field, the example he sets and the leadership he's shown.
"He's able to get open on what seems like every play. I can't be more pleased with him."
Cleveland open their pre-season campaign next week against the St Louis Rams.