The terms of the 16-year-old's move south of the border had looked likely to be determined by the world governing body with the two clubs unable to agree a fee.
Rangers believed they were due more than what Villa were offering and that Wilson remained their player until December.
But he will now join Villa on July 1 after a fee which could rise to around £1million depending on add-ons was agreed.
Wilson, who scored 49 goals at youth level last season, will initially team-up with Villa’s under-18s.
He is the latest of several six-figure arrivals in recent years with Villa’s board viewing a strong academy as key to their long-term strategy.
In terms of the first-team, the club’s focus for the transfer window has shifted for now towards moving players out with Trabzonspor continuing to lead the chase for winger Trezeguet.
The Egypt international made just one substitute appearance in the Premier League last season, spending the second half of the campaign on loan at Istanbul Basaksehir.
Trezeguet has scored nine goals in 64 appearances for Villa and will be allowed to make a permanent exit this summer.