Marine Reservist JJ Chalmers, 25, was badly injured while serving in Afghanistan.
He was with his father for the induction during the morning service at St Giles Cathedral on the Royal Mile in Edinburgh.
The Very Reverend Professor Iain Torrance was at the same time inducted as the new Dean of the Chapel Royal.
As Dean of the Chapel Royal, Professor Torrance is responsible for the oversight of the ecclesiastical establishment, which is part of the Royal Household.
He is also Pro-Chancellor of the University of Aberdeen.
He said: "Today is a very special one, made all the more special for me by the fact JJ was able to attend as he continues to recover from his injuries. I am delighted to be appointed as a Chaplain to the Queen and look forward to fulfilling the duties of this role."
Professor Torrance said he was greatly honoured by the trust placed in him by the Queen.
He said: "I am honoured to take up this role and am looking forward to the challenges and opportunities which it will present."
The service was also attended by former Moderator of the General Assembly of the Church of Scotland, the Very Reverend Dr John Cairns, who has recently retired as Dean of the Chapel Royal and has subsequently been knighted. He was appointed Dean to the Chapel Royal in 2006.
The Right Reverend Lorna Hood, Moderator of the General Assembly of the Church of Scotland and also a Queen's Chaplain, welcomed the appointments.
"Both Iain and John have faithfully served the church with distinction and we rejoice with them in this recognition by the Queen," she said.
"The Church of Scotland is proud of its relationship with the Royal Household and we look forward to maintaining those links in the future."