The move has been described as "historic", and the regulator will make its decision next month.
Doctors want to make babies from three people to prevent diseases that starve the body of energy, leading to brain damage, muscle wasting and heart failure.
However, fresh evidence suggests it will fail in one in eight pregnancies.
Three-person IVF replaces the defective power packs in the mother's egg - called mitochondria - with healthy ones from a donor woman.
