Executive principal Genevieve Simson said the Department of Health and Human Services had completed the risk assessment, and had advised the school could reopen as deep cleaning was completed.
"DHHS has concluded the student was not on site while infectious and therefore close contact tracing was not required in this case," Ms Simson said.
"They have also advised the school can reopen from Wednesday, August 12 now appropriate cleaning has been completed."
Ms Simson thanked the community for their patience and respect for the privacy of the student who tested positive for COVID-19.
"I am proud to belong to such a caring and supportive school community and I thank you for your understanding at this challenging time," she said.
"The school will continue to work closely with both DET and DHHS during this time, and we wish the affected student a speedy and safe recovery."
All Victorian students have been remote learning from Wednesday last week, except for vulnerable students, children of vulnerable workers, and specialist school students in regional Victoria.
Ms Simson said more information about the school and COVID-19 could be accessed on the Department of Education (DET) website or by contacting the DET coronavirus (COVID-19) hotline on1800 338 663, which is operational from 8am to 6pm, seven days a week.
"If you call them, please be clear that you are calling in relation to Greater Shepparton Secondary College, and they will provide as much information as they can," Ms Simson said.
For information in a language other than English is available, call TIS National on 131 450 and then request the DET coronavirus (COVID-19) hotline.