The £11.9 million redevelopment was given the green light by NHS leaders at a meeting in Whitby last Thursday.
Dr George Campbell, a family doctor in the Esk Valley area of Whitby, and a member of the CCG governing body, said: "I feel a huge sense of relief and pride to see these plans get the sign-off by the CCG after years of hard work.
"I'm so proud of the project team who have navigated through the challenges and for the staff and partners who have supported them.
"There has been some anxiety about the CCG's intentions but I hope that this decision demonstrates how much we value the hospital, staff and services. We will continue to work hard with our partners to make these plans come to life."
The decision ends a long period of uncertainty over the future of the hospital, built some 50 years ago as a pioneering small hospital staffed by local doctors, and opened by the late Princess Margaret.
The next step is for the main providers of services at the hospital, Humber Teaching NHS Foundation Trust, and the owner of the site, NHS Property Services, to approve proposals at their board meetings due to take place in the next few weeks.
The proposals for the hospital, perched overlooking Whitby harbour, include an extra care facility to complement the hospital's existing services, large new car parking area, an ambulance bay, facilities for dropping off patients, external pedestrian links, an a plaza to connect the retained hospital tower block.