Verstak was born in Tianjin, China, to Russian couple Vladimir and Valentina Verstak. They immigrated to Australia when she was 10 years old and settled in Manly, New South Wales. In 1961, she became the first migrant to win the Miss Australia title.
Even before going on to compete in Miss International, Verstak's victory in the national pageant was already seen as a small but significant shift in the traditional articulation of the Australian feminine ideal, attributed to the infusion of European values to the Anglo-Australian fabric, at a time when beauty pageants were the craze in Australia.
Verstak went on to win the Miss International title in Long Beach, California. Thus, the victory further endeared her to the Australian public, demonstrating their pride and approval of Tania Verstak as the embodiment of perfect Australian womanhood and as the image of Australia as a modern nation, even though in the terminology of the time for immigrants, she was a "new Australian".
As part of promoting Australia as "international", the Australian "national costume" for the pageant broke away from the British-related image it had until then. Whereas the previous contestant had worn a British riding costume, Verstak expressed this new sophistication when she wore a specially created yellow dress embroidered with a wreath of Australian wild flowers and carried a yellow umbrella.
Verstak's first high profile relationship was with former Channel 7 rugby league commentator, 'sideline eye' Barry Ross. After an acrimonious split, Verstak then met and later married a Perth businessman, Peter Young. Their daughter is the actress Nina Young.