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The 32-year-old, who won a silver medal in the doubles over the same distance alongside Jon Schofield, won his semi-final in a time of 34.076 seconds.
The final will be held on Saturday at 13:07 BST.
Britain also qualified for Saturday's women's kayak 500m final (13:47 BST), coming third in their semi-final in a time of one minute 36.25 seconds.
Heath is attempting to retain the title for Team GB after Ed McKeever won gold in the same event at London 2012.
"That felt really good," said Heath. "I'm feeling really solid right at the moment. To make the Olympic finals is pretty amazing."
Great Britain's Liam Heath qualified second-fastest for the final of the Olympic men's 200m kayak sprint.