Leacock-McLeod is understood have agreed an 18-month deal at Ibrox with the option of a further year.
The 19-year-old linked up with Rangers last month for a trial period and he is thought to have caught the eye during his time in Glasgow.
Leacock-McLeod scored in a practice game against Airdrie and also spent time training with Mark Warburton's first-team squad at Murray Park.
Leacock-McLeod is a product of the Fulham youth system and he left Craven Cottage to join Wolves 18 months ago.
The skilful attacker never made a first-team appearance under Kenny Jackett for Wolves, but he was a regular in the club's under-21 side.
Capable of operating on either flank or as a deep-lying front-man, Leacock-McLeod’s versatility makes him a useful asset to Warburton's side although he is likely to sign as an academy player at Ibrox.
Leacock-McLeod is Rangers' second signing of transfer deadline day following the arrival of Michael O'Halloran from St Johnstone.