Nick Cust, who has been executive chairman since January 2011, steps across to become non-executive chairman.
Liney, who joins in August, was chief executive for STA Travel for eight years having previously worked for eBookers.com, Travel Bag and British Airways.
The move follows ECI Partners taking a majority stake in York-based Amber Travel in April.
Cust said: “As the business has grown and matured rapidly, both ECI and the directors recognised the need for a full time chief executive.
“Peter is an outstanding candidate who will compliment our existing management team and add to the considerable success they have achieved to date.”
Chris Watt from ECI added: “We are delighted to welcome Peter on board as CEO of Great Rail Journeys following our recent investment.
“Peter brings with him a wealth of experience and we are confident he can help maximise the potential of the business working with the rest of the management team. We look forward to working with him to support continued strong growth at Great Rail Journeys and Treyn.”