Professor Green, from the University of Bristol Law School, will replace Stephen Lewis as the Commissioner for Commercial and Common Law for a period of five years from 1 January 2020.
As part of her new role, she will help ensure the Commission keeps abreast of emerging developments in bioethics, cybercrime, big data, security and privacy, artificial intelligence (AI) and the digital economy.
Over and above her work on the use of technology in business and commerce, she will take over the completion of a project on the Right to Manage which aims to make it easier for leaseholders to take control over the running of their buildings.
Professor Green, who joined the Law School in 2017, said: "Technology poses a series of complex problems for lawmakers and wider society. The work the Law Commission is undertaking on such matters as intermediated securities and smart contracts can help unlock obstacles to business, which will be especially important in the trading environments of the future.
"I look forward to joining the Law Commission to tackle these challenges and to assist in shaping the legal reform that will allow these technologies to thrive in the UK."
The Law Commission has also appointed Professor Penney Lewis, who will replace Professor David Ormerod QC as the Commissioner for Criminal Law and will join the Commission.
They both join the Commission at a time of great constitutional, economic, social, scientific and technical change and will be instrumental in leading law reform in England & Wales.
Sir Nicholas Green, Chair of the Law Commission, said: "We are absolutely delighted to welcome Professor Penney Lewis and Professor Sarah Green to the Law Commission. The pool of candidates for the two positions was exceptionally strong.
"Our two new appointments bring with them to their posts tremendous skills across a wide range of subject matters and issues that will be of importance in the coming years. We are all looking forward to working with them."
The two appointments are the first made through a new process which sought to encourage applications from a broader and more diverse range of people than the Commission had traditionally recruited from.
The Commission conducted outreach work with a range of contacts in academia, representative lawyers' groups and other key stakeholders to draw attention to the roles and to encourage applications from those who might not otherwise have considered applying for the role.
The Commission also sought interest from lawyers with skills relevant to the challenges that society will face in the future.