Joseph William Kershaw, 23, was seen in the video on April 8 as he stripped all of his clothes and walked around briefly before getting dressed, The Sun newspaper reported.
His behavior triggered a wave of criticism from Thai people for disrespecting their culture. Some residents reported the incident to local police.
On Tuesday he was arrested at his hostel.
He admitted to the police being the man in the video and claimed he stripped due to "being intoxicated and overexcited," according to British newspaper Metro.
He was fined £110 (US$137) and forced to make a public apology.