The invention will now be made into a real gadget, the Mirror reported.
"One day, to while away the time when brushing my teeth I calculated that on average people spend 75 days of their life with a toothbrush in hand," Baxter, 19, said. "The Odd Invention challenge gave me the chance to share my idea for a gadget to help us use that time more productively."
He beat out 300 other entries to win the contest.
Witt Oddoksi, the founder of Oddka who sponsored the competition, said the toothbrush top hat invention was worthy of winning.
"This revolutionary appliance offers a hands-free tooth brushing experience, allowing the wearer to continue with other tasks," he said.
Other entries included heels that can store keys, a beard shaped razor and and umbrella that can form a pop-up toilet cubicle.