Under the Veterans Interview Programme (VIP), companies promise an interview for jobseeking ex-servicemen and women, along with other forms of employment support for veterans.
More than 20 leading UK employers, including O2, Comet, Crossrail, Greggs, Centrica, John Lewis, Poundland, Wickes and the Scottish Football Association, have signed up to the scheme, set up by shadow defence secretary Jim Murphy.
Mr Morrice said many members of the armed forces, including people in West Lothian, were being made redundant when economic times were already difficult.
He said: “We have a duty to do what we can to support our forces and veterans. It is wrong that someone who has served in Afghanistan is expected to join the back of the queue at the local job centre.
“Initiatives such as this underline our country’s respect and goodwill towards the service community.”