Jersey residents and visitors were allowed to travel without special permission from 3 July.
The process of getting into Jersey could take up to three hours, according to Senator Lyndon Farnham.
The island is opening its borders, but incoming passengers will have to submit to a swab test on entry, or agree to isolate for 14 days - the fine for not doing so is £1,000.
"We are going to be welcoming many islanders back home, many friends and relatives will be coming over to catch up, and some new visitors will be arriving in Jersey," said the deputy chief minister.
"I ask people to be patient - the testing and processing process is very thorough, and it could take one to two, possibly three hours because we need to make sure everyone is accounted for," he added.
The government said it's putting the health and wellbeing of islanders "at the front of all decision-making".
Schools in Jersey have recorded attendance rates above 84% after fully reopening on 30 June.
Primary schools have recorded attendance between 96% and 99%, while secondary schools recorded between 84% and 96% for various year groups.
The government said the specific order and frequency of return for each year group is decided by each individual school head teacher, "based on local priorities, physical set up needs and staff availability".
"These figures are extremely positive and demonstrate the high confidence that children, young people and their parents or carers have in returning to school," said Senator Tracey Vallois, the island's Education Minister.
"I would like to express my sincere gratitude to all of our education staff, students, parents and carers who have made the return to school so successful," she added.
BBC Radio Jersey
Jersey's chief minister suggests the chance of a visitor to the island spreading coronavirus is "low risk".
Senator John Le Fondre was defending the decision to open Jersey's borders, adding the decision was made based on medical advice.
People coming to the island will have to take a coronavirus test, but will not have to isolate themselves while they wait for the results.
He added the "balance of risk" of the policy was about if it was right to "close down" the civil rights of the majority of people by keeping the borders closed.
Mr Le Fondre said: "Asymptomatic people, i.e. those who are not coughing and spluttering, are proven to be less likely to spread the disease, it's not zero risk, it's low risk."
BBC Radio Jersey
GPs in Jersey will not be renewing the temporary roles they took on during the coronavirus pandemic, the organisation representing GPs has revealed.
The Primary Care Body explained this is due to the reduced number of cases of the virus in Jersey and GP's wishes to return to their pre-pandemic services.
During the pandemic the island's private GPs have been employed by the government and subsidies have cut the cost of related fees.
The temporary contracts with Health and Community Services end in August.
He added that Dr Nigel Minihane would like to personally distance himself from the comments made within it and wished to reassure patients who were worried about the claims it made.