Torvalds, a Finn who now works in Silicon Valley, was honoured for his work in developing the open source Linux operating system, while Yamanaka was given the prize for his creation of testing methods for adult stem cells.
The awards were handed out on Wednesday afternoon by President Sauli Niinistö in a ceremony at the Finnish National Opera House.
The prize is awarded biennially by the Technology Academy Finland. Previous winners include Tim Berners-Lee, inventor of the world wide web.
Organisers say the prize seeks to highlight innovations that enhance everyday lives. In addition to money, winners take home mountain-shaped trophies with a crystal tip made from silicon, a matter used in all electronics today.