Green, who has worked for the YMCA for more than 20 years, will replace Rosemary Gillespie, who was asked to stand down from the trust last summer after 15 months in charge.
The charity said at the time that a "change of leadership was needed for the next stage of the organisation’s development". Gillespie said she had been poorly treated and the trust did not "have the stomach for the programme of change I was brought in to deliver".
Green, who will join the charity in March, is currently part of the executive staff team of the World Alliance of YMCAs, based in Geneva.
He was chief executive of YMCA England between 2008 and 2013 and before that spent six years as head of YMCA London South West.
He spent 20 years until May 2010 as a Conservative councillor for Ealing Council in west London, including time as cabinet member for adult social services and housing, leader of the opposition and mayor.
He is chair of Advance, a housing association that works with people with learning disabilities and mental health issues, and is on the board of the West Hampshire Clinical Commissioning Group.
A spokeswoman for the charity declined to confirm what Green’s salary would be.
Robert Glick, chair of the Terrence Higgins Trust, said: "Ian has a track record of strong leadership, and we are confident he will ensure that THT continues as the UK’s leading HIV and sexual health charity."
Green said he had long admired the charity’s work and was honoured to accept the role.
"I look forward to working collaboratively with staff and volunteers, the board of trustees and all external partners to continue to deliver innovative HIV and sexual health services across England, Scotland and Wales, in what are undoubtedly challenging times, with cuts to health and social care budgets," he said.