James Samuel Willis, originally from Stockton but now based in the Gosforth area, and two 16-year-old girls were believed to have been using an inflatable dinghy when they got into difficulty yesterday.
They were on an adult-supervised trip from St Nicholas Hospital in Gosforth, Newcastle, which is a medium secure psychiatric unit for youths.
It is run by Northumberland, Tyne and Wear NHS Trust, where a spokesman said staff were "devastated".
The unit cares for 14 to 17-year-olds who have either come into contact with the law as a result of their mental health issues, or are a risk to themselves or others.
The spokesman said: "We are all shocked and devastated by the news.
"We have spoken to his family to offer our sincerest condolences at this difficult time.
"We are fully co-operating with North Yorkshire Police to assist them in their investigation."
The group got into difficulty near Whitby's West Pier just before 1pm yesterday.
The 17-year-old had managed to clamber up a ladder on the wall but went back to help one of his friends and was hit by a number of waves.
He was pulled from the water unconscious and was flown to Scarborough District Hospital where efforts to revive him failed.
The girls escaped with minor injuries and were discharged from hospital later.
At inquest into the teenager's death is expected to be opened and adjourned tomorrow.
North Yorkshire Police launched an investigation and witnesses were asked to call 0845 606 0247.
Katie Gellatly, Humber Coastguard watch officer, said: "This incident reminds us all of the hidden dangers present when swimming at the beach, and we would urge all members of the public visiting the coast to use lifeguarded beaches where possible, and take note of any signs or flags that show which areas are safe to bathe in."