The head coach ended his three-year spell at Cardiff Blues on a triumphant note last month as they sealed a European Challenge Cup final win over Gloucester.
Wilson had agreed to link up with Premiership side Wasps to work with director of rugby Dai Young and a deal appeared to be set in stone.
However, he has had a change of heart and decided to replace Ulster-bound Dan McFarland in Scots' coach Gregor Townsend's backroom team.
"To coach international rugby and go to a Rugby World Cup is obviously the pinnacle of the sport and the goal of most professional coaches,' Wilson said. 'It was therefore a huge honour to be identified by Scotland and offered this role.
"This has obviously been a little unexpected and happened very quickly, so I'd like to thank Dai Young and Wasps for their consideration and understanding of this situation and wish them the very best of luck for the future.
"I think Scotland have made huge strides in recent years and play an exciting brand of rugby, with an ever-growing, quality player base.
"I'm really looking forward to working with and learning from Gregor and the rest of the staff and players in Scotland."
In response to the news, Young said on Monday: "This is a big disappointment for us. In addition, the timing could not be much worse.
"Finding someone of Danny's quality and experience who is available at this time of year to supplement our existing coaching team is a difficult proposition.
"Disappointing as this is, I understand that the opportunity to coach a tier one international side through to and beyond the World Cup would always be difficult to turn down as opportunities like this do not come around very often."