The 23-year-old has been on trial at the Scottish Championship side this summer along with former Hearts midfielder Jason Holt, while James Tavernier and Martyn Waghorn have also been linked with the Ibrox club.
Halliday scored 15 goals as a teenager for Livingston before moving to Middlesbrough in 2010, where he made 44 first-team appearances.
The Scot joined Bradford in January following a loan spell and scored in their shock FA Cup victory over Chelsea at Stamford Bridge.
Warburton said: “Andy’s done very well and is in the process of signing for Rangers Football Club, which I’m delighted about.
“He is 23 years old, good number of league appearances under his belt already for a young player. He will bring good quality to the squad.”
Although he has been busy looking at players, including those on trial, Warburton is determined only to sign players who add value to the club.
“We are looking at people,” the former Brentford boss added. “It’s not about numbers. People get confused about adding numbers to a playing squad, you add quality.
“We are still relatively light. We are hoping to make two or three moves in the days and weeks ahead. We are working on a number of targets. At this time of year, there are a number of clubs looking at the same players.”