The Swans face League Two Bradford in the Capital One Cup final, less than 10 years after beating Hull on the final day of the 2002-03 season to retain their Football League status and stave off the threat of possible extinction.
Jenkins has been involved at every step of that recovery.
He came on board as part of the consortium brought together through the then newly-formed Swansea City Supporters' Trust, which managed to force unpopular Australia-based businessman Tony Petty out of the club in January of 2002.
Since then, Jenkins has overseen the club's rise up the league ladder and the switch from the Vetch Field to their current Liberty Stadium home.
He has proved himself particularly shrewd when it comes to the appointment of managers, bringing in the likes of Roberto Martinez, Paulo Sousa, Brendan Rodgers and current boss Michael Laudrup to ensure the club's attractive style of play is continued.
Jenkins has also kept a firm handle on club finances, and the debt-free Swans announced a record profit of £14.6 million after their first top-flight season.
Supporters' Trust spokesperson Alan Lewis believes Jenkins has made the greatest contribution of those who have turned the club's fortunes around.
Lewis told Press Association Sport: "I am sure his fellow board members would say themselves that Huw deserves huge credit. Huw has probably put in as much time as anyone in getting the club to where we are now.
"He would admit himself that when the consortium got together he ended up as chairman as no-one wanted to do it, and none of them had ever run a football club, even though they were businessmen.
"It was a huge personal effort on his behalf and the club ethos he has put in place is one all the directors sign up to and he leads the way in that. His contribution has been as significant, if not more so, than anyone in this story.
"He has had to manage the profile of the club, which is as high as it has ever been, and make sure the future is a sustainable one whether the club had survived in the Premier League or not.
"It's quite incredible what has been achieved, you could not make it up frankly, and if you did no-one would believe you, it's ridiculous really."
Swansea's Supporters' Trust holds a 20 per cent stake in the club, and has been highlighted as an example for others to follow.
The Trust has a representative, Huw Cooze, on the club board, making Swansea the first side in the Premier League with an elected supporter serving as a director.
Their formation came during a period when the club was sold for £1 twice in a matter of months in 2001. Firstly, commercial manager Mike Lewis bought the club from a London company called Ninth Floor, whose main business was making windows.
But the debts of £800,000 proved unmanageable and Petty quickly took over, flying in from Brisbane and attempting to sack seven players and two coaches to cut costs.
"We formed in August 2001, and even before Petty came in the writing was on the wall," said Lewis.
"There was a company called Ninth Floor who were not interested in the club and there were huge debts. We needed to get our act together otherwise we would not have had a club to support.
"Supporters Direct got involved and helped us and it grew from there.
"We played a pretty big part in bringing the consortium together to save the club and we were one of the signatories on the consortium's deal.
"We initially needed £50,000 for our shareholding contribution, and within 12 months we had put £100,000 into the club and that increased as more shares became available to £200,000, which gave us our current 20 per cent share."
Lewis added: "We have had contact with dozens of other supporters' trusts, but obviously we had a very specific set of circumstances at the time we were formed.
"There is no checklist you can follow as those dire circumstances in 2001 were what gave us the opportunity to get involved.
"But, if we are held up as an example to others then that is great. As a Trust and a club we never imagined we would be where we are and obviously if it can happen here, then why can't it happen for other clubs?"