Spieth, 21, has enjoyed a breakthrough year in 2015 winning both the Masters and the U.S. Open and will be among the favourites at the British Open which begins at St Andrews next week.
Woods, a 14-times major winner, dominated the sport for more than a decade and Azinger said Spieth had shown enough in his fledgling career to suggest he is capable of emulating his compatriot.
"He's all the things Tiger was," Azinger, an ESPN analyst for the British Open coverage in the U.S., told reporters on Wednesday.
"Tiger was as composed as anybody and if he did get ticked off he was able to put it behind him. Tiger was strategic and studied, he knows a lot about the game and Jordan reminds me in that part. He shares what he's thinking and I think that's just great.
"My favourite thing about Jordan Spieth is he is who we think he is. He's just a good guy who has got his act together.
"He's an old head on a young body. He's strategic in his approach and he just seems grateful; he works for everything he's got.
"He's a breath of fresh air."
World number one Rory McIlroy announced on Wednesday that he had withdrawn from the Open at the home of golf after he suffered ankle ligament damage during a football match with friends.
In the absence of four-times major winner McIlroy, Azinger said the St Andrews course would suit Spieth in his bid to add a third major to his rapidly growing collection.
"I think he's got his own things to deal with whether Rory is there or not," he added.
"The golf course sets up nicely for him. It's hard to get it close at St Andrews and he's the best in the world between 15 and 25 feet."
(Writing By Tom Hayward; editing Toby Davis)
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