To obtain a sample, the user must pay via the app, which will allow the sperm to be delivered to a fertility clinic of the woman's choice.
Dr Kamal Ahuja, scientific director of the London Sperm Bank, told the Sunday Times finding a donor will now be as easy as ordering from big retail websites such as Marks & Spencer or Tesco.
He said: 'You make all the transactions online, like you do anything else these days.
'This allows a woman who wants to get a sperm donor to gain control in the privacy of her own home and to choose and decide in her own time.'
But it has been criticised by campaigners, including Josephine Quintaville of Comment on Reproductive ethics, who told the paper: "It's digital dads. This is the ultimate denigration of fatherhood."
Women using the app can list the characteristics they most desire in a father and can set up alerts when an appropriate person becomes available.
Among the anonymous donors are lawyers, doctors, engineers and actors.
The app has met all the criteria set by the Human Fertilisation and Embryology Authority (HFEA), which regulates in vitro fetilisation (IVF).
It is understood around half of the UK's private and NHS IVF clinics have registered with the service.
The London Sperm Bank, which was previously the Dr Louis Hughes sperm bank set up in 1976, was formed when the latter joined forces with the London Women's Clinic sperm bank in 2010.
A statement on its website said: "The London Sperm Bank (LSB) was established to address the acute shortage of donated sperm in the UK. With support from a wide range of altruistic men, we are proud that we are now the largest provider of donor sperm in the UK."