The Irishman has signed a three-year contract, which takes effect when the Irn-Bru Third Division champions' transfer embargo expires on September 1, after a six-and-a-half-year stay at Dundee United.
The striker, who followed Kilmarnock goalkeeper Cammy Bell and Motherwell midfielder Nicky Law in joining the Glasgow giants this week, scored 72 goals in 203 appearances for United, some of those from centre-back.
The 30-year-old told Rangers TV: "I've a lot of time for Ally and his coaching staff and to go on to play for them is a big thing.
"When we met for the first time, I could see the passion the manager has for the club and he really wants to drive it forward.
"He spoke to me about the crowds and the club's history and once we'd had a chat, my mind was basically made up.
"I didn't really want my agent to speak to any other clubs, I wanted to try to get this deal over the line and thankfully that has happened.
"Having spoken to Ally, there's no doubt where I want to play my football and I'm really excited about what lies ahead.
"I've taken a step back in terms of the level of football I'll be playing but in terms of club size, Rangers are massive.
"There's a huge fanbase and when the chance came up to come here it was a no-brainer for me. It was a challenge I wanted to take on."