Paramedics who were quickly on the scene pronounced him dead. An investigation into the accident has been launched.
Kanet Chansong, a security guard who was standing close by when the tragedy occurred, said: “I heard the sound of the tree and I thought it was a fallen branch hitting the ground.
“A woman screamed so I walked over and realised it was a person. They were dead. I saw that they had jumped from the building.”
It is believed Odinson was born in Cambridgeshire but had been living in Thailand and working at a skydiving school in Pattaya for some time, helping customers complete tandem jumps.
Friends from the skydiving community and clients of the school took to social media to pay tribute to Odinson.
But Thai police said they would be investigating how he came to conduct the illegal base jump in a busy area of the built-up coastal city.
Staff at the Lumpini Ville Naklua tower block said it was not the first time he had leapt from the roof of the building.
A security guard at the property said: “They were making video content for social media. They had done this before and they knew it was not allowed.”
Police Lieutenant Kamolporn Nadee, deputy inspector of investigations at the Bang Lamung district police station, said: “The parachute that the deceased used to jump malfunctioned and was not centred as expected. He was in a terrible state when we arrived.
“The friend who recorded the video of him jumping was questioned and the video was examined as evidence.
“Forensics officers are investigating the case further. They are examining the parachute.”
Police said they had informed the British Embassy in Bangkok, which would be contacting his family in the UK.
A spokesman for the Foreign Office said: “We are supporting the family of a British man who has died in Thailand.”