Anthony Nolan co-ordinates transplants for the NHS, collecting and delivering cells to hospitals across the UK and sending cells abroad. It is involved in more than 1,000 UK transplants between donors and unrelated recipients each year and sends cells abroad to another 300 patients.
Ms Alderson said prior to the new centre, the charity had struggled to get stem cells collected "at the time the clinical community need us to".
"It is only one in five times where we have been able to get collections to donors on the day doctors have asked for them," she added.
She said when recipients saw a bag of stem cells, "it is an incredible moment".
"Ultimately, that small bag can save someone's life. It is a bag of magic," she added.
"We will make sure [donors] have the best experience at our new centre."
The centre has been part-funded by Omaze, which partnered with Anthony Nolan and raised £3.7m through a house prize draw in June.
It is estimated the money will help fund the centre's work for 18 months.
Kathryn Fairbrother, director of clinical operations for research and innovation at Nottingham University Hospitals (NUH) NHS Trust - which runs the QMC - added: "There are opportunities for Anthony Nolan and for ourselves to do research that we wouldn't have done before."
One of the research projects planned involves using stem cells to treat liver disease.