In a photo finish, Heath edged out Hungary's Kolos Csizmadia to secure his third consecutive medal at an Olympic Games in a time of 35.202 seconds.
The 36-year-old also set an Olympic-best time of 33.985 seconds in qualifying.
Following the race, Heath spoke to BBC Sport:
"I was maybe a bit hesitant off the start and didn't reach my potential in terms of peak speed.
"I am still happy with the performance. It is hard [another medal] to put into words. It is what you work towards to be at your best for these events."
Heath graduated in 2006 with a degree in Industrial Design and Technology and was awarded an Honorary Degree from the University in 2018.
Heath’s bronze is º¬Ðß²ÝÊÓƵ’s tenth medal at the 2020 Tokyo Olympic Games, which includes three golds, five silvers, and two bronze medals.