The Scottish club completed the transfer of the Croatian midfielder on Thursday following a stint in the North American Soccer League with New York Cosmos.
Warburton believes the former QPR, Portsmouth and Tottenham man will bring with him to Ibrox an enormous amount of technical ability and overall quality.
"We are getting a 31 year-old player who has a real appetite for the game still," he told the club's official website.
"I went to see Niko in New York and it was important for me to hear how hungry he is – and I was delighted with that response. He is a player who has so much to offer, and I think Ibrox and Rangers gives him a fantastic stage to express the quality he has.
"He is a very technically gifted player, a player who sees a pass and one that can open up defences with the quality he possesses.
"He gives us something different – we have some tremendous players in that squad but we are always looking for variety, and he has that."
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