The Post and Courier of Charleston reported that officials had said earlier this month they were unsure if they could make the move to new buildings by the start of the classes in August.
The school district's Bill Lewis said Tuesday the move will be completed in time.
The district decided earlier this month to move the five affected schools to other facilities in Mount Pleasant and North Charleston.
Engineering reports showed the five schools' current buildings would threaten children's safety if a moderate earthquake struck. The school board says students will be able to return to new buildings by the 2013-14 school year.