The 51-year-old's five-year spell at Bramall Lane came to an end last month in confusing circumstances.
Wilder's departure by mutual consent was eventually announced by the club around 48 hours after rumours began emerging that he would be sacked.
When I walked back into Bramall Lane, in May 2016, having been given the chance to manage the Club I'd supported all my life, who could have predicted the next four-and-a-half years?" he said, via a statement on Instagram.
"It has been some journey and one I'm immensely proud of."
"As proved this season, football is just not the same without fans and I stand by the comment that I've made on numerous occasions, the Club have missed out more than most, Unitedites have the ability to turn losses into draws and draws into wins.
"I cannot stress enough how important the fans are and I've been humbled by the unequivocal support, even this season when things haven't gone so well."
Since his exit Wilder has been linked with other roles, including the vacant job at Celtic, but insisted he has no immediate plans to get back into management.
He added: "I would like to wish everyone associated with the football club & the owners the very best in the future. This Football Club will always hold a special place in my heart, it has from an early age and that will never change.
"Thanks again for everything."