The 19-year-old took in Hibs' 1-0 victory over St Mirren on Saturday and is expected to complete his move to the club within the next 24 hours.
The Daily Record is reporting that Middleton is at Hibs' East Mains training base to finalise the deal and that Paul Heckingbottom's side have beaten off competition from Dutch side NAC Breda for his services.
Middleton is a pacey, direct winger who played 28 times for Rangers last season and most notably scored against CSKA Moscow in the Europa League.
The former Norwich City youngster would be unable to feature for Hibs this weekend as they face Rangers at Ibrox, with the player likely to be in the Hibs squad for the Betfred Cup tie against Morton on August 17, assuming there are no issues discovered during the medical.
Middleton has become a top target for Hibs after Australian winger Martin Boyle was ruled out for several months due to a knee injury. He is due to have surgery on Tuesday.