Woods was unveiled as the man to replace Mike Newell yesterday after beating off competition from five other short-listed suitors, including Russell Slade, John McDermott, Lee Richardson, Gerry Taggart and Gary Brabin.
And, while admitting it was a big decision for the future of the football club, the chairman feels the board has made the right choice in Woods.
Mr Fenty said: "It's a huge decision and we didn't want to be having to make it again so soon after the last time.
"It's easy to go for the tried and tested and appoint people who are looking for better horizons.
"We felt for some time now that there needed to be some restructuring.
"The fact of the matter is that we are crying out for stability at the football club, there's no doubt about that.
"After a raft of applications for the manager's post, the board of directors dismissed the journeyman and those that are likely to get itchy feet during the contract.
"Our assessment of the young and hungry untested managers actually showed there was an awful lot to offer.
"It's a breath of fresh air to have Neil here."
Woods has been in caretaker charge since Newell's sacking last month but has failed to register a victory in six league and cup games.
But the chairman is confident the shoots of recovery have been slowly bursting through and has high hopes for his new man at the helm.
Mr Fenty added: "From a side that was shipping goals with no shape and several square pegs in round holes, Neil has achieved the first steps in restoring confidence in the players.
"He has achieved back-to-back clean sheets in a week.
"In fact, we have seen more football in the last three weeks than we have for many months.
"That paints a picture of where we are at and I'm sure things will get better with the hard work that Neil continues to put in."