Cole will be joined by former Telegraph editor-in-chief John Bryant, who will chair the Trust, and former BBC World Service director of English networks Philip Harding.
The trust was created as an additional safeguard for the news agency’s editorial independence, as PA Group has diversified into commerical markets.
It will produce an annual report for PA Group’s board on The Press Association’s adherence to its core editorial principles.
The trust will also meet the PA editor-in-chief and editor to discuss the agency's editorial coverage, and act as a sounding board for the editorial team.
Bryant said: "The expansion and diversification of the roles played by PA Group means that this is a challenging moment to set up The Press Association Trust.
"The integrity and core values of The Press Association will be ever more important as PA Group moves to serve the growing and varied demands of its customers, both in print and electronically. I look forward to working with Peter and Phil on this challenge."
Bryant has 40 years' experience in the newspaper industry. He began his career at the Edinburgh Evening News and went on to be deputy editor of The Times. He also held senior posts at the Sunday Correspondent, the European, and the Daily Mail.
Cole was founding editor of the Sunday Correspondent and deputy editor of The Guardian, and has held senior editorial positions on the Sunday Times and London Evening Standard. He is on the board of the National Council for the Training of Journalists and the Society of Editors.
Harding has held a variety of senior editorial jobs in BBC radio and television. He is a former editor of the Today programme and controller of editorial policy at the BBC.