"You'd never say Rhys didn't take the opportunities that life provided for him."
The college's chief executive, Charlie Phillips, said the college community was deeply saddened by the news.
"He had the right balance of cheek and respect, was a very popular student and was fundamentally a good bloke."
Mr Cochrane, who was raised in Hahei in the Coromandel region, graduated from the college in 2012 with an adventure tourism diploma.
He made international news in 2012 when he risked his life to rescue an orca tangled in fishing net debris off the Coromandel coast.
Mr Phillips said that episode "speaks volumes as to his character".
Mr Cochrane's employer, Hemisphere Crew Solutions, announced his body had been found on Thursday. A company statement said Mr Cochrane was a competent and experienced swimmer and diver.
"Swimming from the yacht was not an unusual thing for him or the crew to do on a daily basis," the company said.
- Additional reporting: NZ Herald