The Bucks have gone for the former Brackley Town manager, who replaced Paul Carden after he became the seventh National League North managerial departure of the season so far on Sunday.
The club went down 3-2 at Peterborough Sports on Saturday and are without a victory since the opening day of the season.
Wilkin has made a quick return to the game and will be joined at the New Bucks Head by his management team at Brackley, Mark Noon and David Staff.
Carden was dismissed a few weeks short of a year in the job, having taken over from Dennis Greene in November 2021.
The FA Trophy winner, pictured, has made his first goal dragging them club away from trouble at the foot of the table.
Telford - out of the FA Cup after defeat to Chasetown - now do not play until October 22 when they face high flying Scarborough and the new manager has plenty of time to prepare his team.
He told the club’s website: “I’m honoured and proud to be appointed as the first team manager of AFC Telford United.
“This will be a challenge in the short term, and we will be looking to work together to make improvements quickly and in the first instance to move to a position of safety, before progressing to a much better future.”
Chairman Andy Pryce said: “He has a fantastic record at our level and above and we will be working with Kevin to progress our on the field results both short term and longer term.”