He is currently the Christian development agency's Disaster Management Director, and succeeds Peter Grant, who has been in the role for five years.
Grant has resigned as International Director in order to set up Restored, a new alliance of Christians working to end violence against women.
Tearfund will host Restored over the next three years, as it builds up its own capacity and identity.
Bainbridge has worked in the NGO sector over 20 years and has worked in various roles for Tearfund, with a particular focus in disaster management and working with local partners.
Among his achievements, Bainbridge led Tearfund to become the first UK agency to achieve certification with the Humanitarian Accountability Partnership (HAP).
Matthew Frost, Tearfund’s Chief Executive, said: "David is passionate about Tearfund’s vision and our focus on the role of the local church in serving people who are living in poverty.
"He is an outspoken and very effective advocate for beneficiary accountability, and has a great track record in building teams and leading and motivating people in very demanding circumstances."