Steven Gerrard has been an admirer of the defender who Rangers have pursued for well over a month.
Edmundson handed in a transfer request at Oldham in order to help push through a deal after Rangers reportedly had a pair of offers turned down.
Earlier this week it emerged that an offer, thought to be in the region of £650,000, had been accepted.
Other clubs in England had been interested but it is understood the 21-year-old had his heart set on a move to Glasgow.
He joins Steven Davis, Jake Hastie, Jordan Jones, Greg Stewart and Sheyi Ojo in signing for the Light Blues this summer.