Three other men were injured just after 08:20 BST near Warsash Maritime Academy, off Hamble, Hampshire.
The teenager was taken to hospital in a critical condition, the ambulance service said.
It was reported the boat had crashed into a marker buoy and capsized, the Maritime and Coastguard Agency said.
The coastguard received multiple 999 calls about the crash.
Eyewitness Ray Dittrich said: "The boat came clean out of the water like a rocket and then it flipped over and landed on its back."
Mr Dittrich, who was fishing on his boat nearby, said he and the crew of another vessel helped pull the speedboat's passengers from the water.
French national Daniel Ubertini, 66, was working at a yacht charter company in Hamble and photographed the crashed.
He described conditions on the water as "very calm ... with not much wind" and said he had seen the craft heading towards the Isle of Wight.
"On her way back I did follow the boat constantly until she started to fly.
"Ten minutes minutes later four or five boats were on the scene plus a helicopter from the coast guard for assistance."
A teenager has suffered life-threatening injuries after the speedboat he was travelling in crashed and overturned in the Solent.