The Scottish Government has approved the outline business case for the £36.4 million centre for the Scottish National Blood Transfusion Service (SNBTS).
Director Mary Morgan said the facility would allow scientists to pursue work to discover new technologies that could "transform patients' lives".
As well as blood, the new centre will test other donated tissues – such as skin, bone and heart valves – helping ensure the future supply of these for patients across Scotland.
Ms Morgan said: "SNBTS is one of the oldest blood services in the world and has been at the forefront of innovations for decades.
"This is a very exciting time for the development of life sciences in Scotland.
"This new national centre enables us to modernise not only to carry on providing safe blood, tissues and cells, but also to continue to pursue and discover vital new cellular technologies which can transform patients' lives in the years ahead."
The new centre, to be built at Heriot-Watt Research Park at Riccarton, near Edinburgh, will centralise the testing and processing of blood and tissue donations.
It is due to be completed in 2017 and is part of more than £32 billion being invested in improving NHS facilities over the next three years.
Health Secretary Alex Neil said: "Having the right facilities in the right place is important to people across Scotland, and that is why we are determined to ensure our blood service is delivered from state-of-the-art facilities."