The aim is to prevent devastating inherited diseases caused by abnormal genes in the mitochondria of human cells.
The proposal was approved by the Human Fertilisation and Embryology Authority (HFEA). The first mitochondrial replacement therapy (MRT) patients could be treated as early as next spring.
IVF babies born through MRT would receive 0.1 per cent of their DNA from a third person besides their mother and father.
The board members of the HFEA met in London to decide whether clinics should be free to apply for permission to carry out the treatments.
They voted unanimously in favour of the treatment.
Christian ethicist Josephine Quintevalle told Premier: "We should be very, very worried.
"This is probably one of the first times that the Christian approach to these issues has been met with the secular scientific concerns around the world".
A team from University of Newcastle is hoping to treat up to 25 women a year with NHS funding.
Critics say the technique is unsafe and faulty mitochondria may still be "carried over" into the child.
Christian Concern's Roger Kiska said: "The HFEA are literally using UK citizens as guinea pigs.
"I mean let's be clear here, the procedure alters the human germline. Whereas most Genetically Modified crops for commercial use are illegal they are now wanting to make legal genetically modified children.
"The free agents used in the procedure are illegal for private use because of their toxicity. They can cause serious or fatal defects there's a high risk of cancer or tumours. We have no idea what it would do for future generation. There are such health and safety risks that this simply isn't viable option."
Last year, the UK became the first country in the world to legalise mitochondrial replacement after MPs and peers voted to allow it.
Asked for his message to the fertility regulator Christian bioethics campaigner James Mildred said: "What were you thinking?
"Why do you think it's ok to breeze past this ethical line in the sand again and again and again.
"Scientists and the evidence that we do have points to the fact that this new technique is reckless and dangerous and will have untold consequences.
"Eminent scientists have warned that a three parent baby will have to be monitored their entire life to make sure that they are healthy, to make sure that they are ok.
"This is a dangerous step in completely the wrong direction."