Vaccinations started on Monday and schools will notify parents and carers of the date that the jabs will be administered, chiefs have said.
Parents and carers of eligible children have been asked to return completed consent forms as soon as possible as the roll-out gathers pace.
Councillor Dr Michael Hardacre, Wolverhampton Council's cabinet member for education and skills, said: "We are working closely with schools and health partners to co-ordinate the vaccine programme in secondary schools.
"Vaccinations are now underway, with the aim of offering either a second or first dose to all eligible children in the next few weeks. Teachers and support staff can also get a jab in school, if they are due one.
"To make sure your child doesn’t miss out, please complete and return your consent form as soon as you receive it."
In addition to second doses, vaccinations are available in school to students who are eligible for, but have not yet had, their first dose, while staff can get a first or second jab, or their booster. Alternative arrangements are being made for children who are home-schooled.
There must be a 12-week gap between first and second doses for 12 to 15-year-olds, or eight weeks for children who are more vulnerable to Covid-19. Pupils who have contracted Covid-19 since having their first dose must wait 12 weeks from the date of their positive test before having their second jab.
Parents or carers who would prefer their child to receive their vaccine outside of school can attend one of a number of clinics, including in the Mander Centre and at Aldersley Leisure Village.