The Bridget Ogilvie Building will contain both the Sanger Institute's sequencing facilities, and the sequencing operation that is delivering Genomic England's 100,000 Genomes Project.
The Biodata Innovation Centre will house start-up genomics companies. Some of these will be spun off from local academic research groups, while others will come from elsewhere in the world. Already businesses from the US, Europe and Asia have moved to the Centre to collaborate with UK scientists.
Mrs May described what she had seen as "an excellent example of research from across the UK and around the world coming together with commerce to deliver benefits for everybody, including patients in the NHS".
"We want the UK to be the 'go to' place for scientists, innovators, businesses and investors," she said. "This really is a very good example of that."
"Genome sequencing is already changing the face of medicine, making possible more accurate and personalised treatments than ever before," said Wellcome's Director Dr Jeremy Farrar. "Wellcome is delighted to build on its support of over 20 years standing with the launch of the Sanger Institute's new sequencing and business incubation centres, which will accelerate further the application of genomics to human health and create significant economic benefits for the UK."