Micky Mellon’s side were promoted to League One after Saturday’s 1-0 win at Cheltenham.
They are second, two points behind Burton, in the hunt for the League Two title ahead of Saturday’s final day clash with Plymouth.
Williams moved to Shrewsbury from Blackpool last year and believes his first season at Greenhous Meadow has been perfect.
“It’s got to be my biggest achievement because I’ve come into a football club as a chief executive for the first time and it couldn’t have gone any better,” said Williams.
“To come into a club that’s been relegated and be stood on the penultimate day of the season having being promoted has to be my biggest achievement.
“But it’s not about me, it’s about Shrewsbury Town and keeping the club moving forward.
“We’ve got a great set of supporters here and it is days like that which make you realise how much Shrewsbury Town means to so many.”
And Williams praised boss Mellon after he came in and overhauled the squad last summer following relegation from the third tier.
“It’s been a fantastic effort. You have to congratulate Micky, Mike Jackson and the rest of the coaching staff as well as the players and credit has to be given to the chairman and the board of directors for the support that they’ve given,” he told the club’s official site.
“He (Micky) has been magnificent. When I came down to see the chairman at the end of last season we discussed potential managers and I suggested that he should have a coffee with Micky Mellon who was someone I knew well.
“He did a fantastic job at Fleetwood and put a football club into the community. He was unfortunate to leave Barnsley after doing a great job at Oakwell.”