The Heyworths have been praised for their protection of the island
The States of Guernsey will have the final say over who the new tenants of Herm Island will be.
Current owners Penny and Adrian Heyworth are selling the remaining 40 years of their lease on the island.
The States of Guernsey owns the island which is about 1.5 miles long and less than half a mile wide.
Housing Minister Dave Jones said he wanted to reassure islanders that all applications would be considered very carefully by the States.
He said the conditions of the lease would have to go before the States as a whole.
"Because it is such a huge part of Guernsey people's life and the island is owned by the Guernsey people, they want to make sure it's protected," he said.
The decision by the Heyworths will bring to an end the longest tenancy in Herm's history.
The lease was taken on by Mrs Heyworth's father, the late Major Peter Wood, in 1949.
Mrs Heyworth, who was born in Herm, said the decision had been an emotional one, but was made because the couple's children did not want to take over the lease.
Deputy Francis Quinn said the family had worked tirelessly for the benefit of Herm.
The island attracts thousands of visitors in the summer
"I think it's a said day for Guernsey and Herm," he told BBC News.
"Nobody, but nobody could have their heart more in an area than Penny and Adrian.
"It's not been a job - it's been a labour of love."
Herm, which is a British Crown Dependency, relies on summer tourism for income. It is only accessible by boat.
The agent handling the sale of the lease, Nick Renney of Martel Maides, said the island's natural charm and the beauty of its beaches was its unique selling point.