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The 30-year-old lost the first round of three but Dychko, 26, tired and Joyce took a unanimous win.
Joyce will face Frenchman Tony Yoka for the gold medal at 19:15 BST on Sunday.
"I'm staying hungry and staying humble," said Joyce. "One step closer - keep it simple and keep on winning."
Losing semi-finalists Dychko and Croat Filip Hrgovic both receive a bronze medal.
Team GB are aiming for a second successive men's super-heavyweight Olympic title after Anthony Joshua won gold at London 2012.
British Olympic boxing champion Anthony Joshua:
"Dychko came out jabbing at the start but Joe broke him down. I am so happy for him. He has come from grassroots and is in the final. I am so happy.
"He is like a steam train, he was flying at the end. We are going to call him 'Steam-train Joe'."
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Great Britain's Joe Joyce will fight for an Olympic gold medal after beating Kazakhstan's Ivan Dychko to reach the men's super-heavyweight boxing final at Rio 2016.