The two animals incorporate a gene that makes them produce a human protein in their milk.
Humans who lack the protein, called alpha-1-antitrypsin, are at risk from the lung disease familial emphysema.
The protein can be extracted from the animals' milk and used to treat patients.
Patent application
The breakthrough promises a big improvement in the practice known as "pharming".
The lambs, Cupid and Diana, were created by PPL Therapeutics, the British biotechnology company spun-off from the laboratory which created Dolly the cloned sheep.
Dr Ron James, managing director of PPL, described the development as "a major technical breakthrough".
PPL said it had filed patent applications for the technique that could generate licensing income in the future. The company's shares rose 5.5 pence, or 6.2%, to 95p in London following the announcement.
Cloning technology
The human gene was inserted using a new technique called gene targeting which replaces one gene with another. Cloning technology is then used to "copy" the genetic changes into a line of identical animals.
"The range of applications for gene targeting is huge and could bring very real benefits for human healthcare," said Dr Alan Colman, PPL's research director.
"For PPL, gene targeting and its applications was one of the key reasons for our involvement in cloning in livestock."
Dr James added: "The real importance lies in the potential application of the technique to provide PPL with therapeutic products for clinical trials more quickly and with more certainty."
Modified pigs
By inserting a gene at a specific chromosomal site, scientists can increase the expression of that gene. This means more of the protein is produced in the milk of the animal.
PPL believes that gene targeting might also be used to replace or inactivate genes.
For example, in xenotransplantation, the inactivation of a specific gene in pigs could make the animals' organs more acceptable to the human immune system.
The company says it has already used gene targeting to switch off a relevant gene in cultured pig cells.