The technical name for these drugs is an antibody-drug-conjugate.
This therapy was developed by GSK in the UK with early research taking place in Stevenage and the first clinical trials in London.
Prof Martin Kaiser, team leader in myeloma molecular therapy at the Institute of Cancer Research, said these "are very smart drugs" and the difference in side effects compared to other drugs "is really remarkable".
While myeloma is still considered an incurable cancer, Prof Kaiser says drugs like this are "an important step towards a functional cure" and he thinks long-term remission will go "above 50% in the next five years".
Antibody drug conjugates are being developed for a range of cancers. The limitation is being able to design an antibody that can target the cancer alone. There is one that can target some types of breast cancer. Research is already taking place on stomach and bowel cancer.
Shelagh McKinlay, from the charity Myeloma UK, said the approval would "transform the lives of thousands" and it was "fantastic to see the UK at the forefront of myeloma treatment".
Health Minister Karin Smyth, said: "This ground-breaking therapy puts the NHS at the forefront of cancer innovation."