There have been ongoing industrial problems in the school for months.
The panel consists of leading educationalist Prof Sir Robert Salisbury, trade unionist John Corey and Belfast Metropolitan College's principal Marie-ThÃ©rÃ¨se McGivern.
Education Minister John O'Dowd has said he wants them to complete the investigation by early summer.
The secondary school, in the Andersonstown area of west Belfast, has 1,100 pupils.
About a third of its 70-strong teaching staff were absent for a period prior to Easter, and, in an unusual move last month, an associate principal was appointed to the school.
A group representing some parents also held a number of protests to express their concern about how the disputes were affecting their children.
Mr O'Dowd said that he wanted the panel to investigate events in the school, and make recommendations "to ensure the school's future".
"I consider the panel members to be eminently well qualified and experienced," he said.
"My priority continues to be to the pupils at the school and this investigation will give pupils, parents, staff and their representatives, and all those involved with the governance of the school, the opportunity to express their view."
The investigation will look at staff relationships, the role of senior leadership, governance of the school and the impact of the ongoing disputes on pupils.
Mr Corey was general secretary of Northern Ireland Public Service Alliance (NIPSA) union from 2003-10 and is currently a member of the Northern Ireland Human Rights Commission.
Prior to her role at Belfast Metropolitan College, Ms McGivern was director of development at Belfast City Council.
Sir Robert, meanwhile, recently chaired the literacy and numeracy task force in Northern Ireland and is a former professor of education at the University of Nottingham.
The National Association of Schoolmasters and Union of Women Teachers (NASUWT), which represents almost half the teachers at De La Salle College, welcomed the appointments.
It said the move "should reassure all partners in the De La Salle community that Minister O'Dowd is committed to finding a robust resolution to the recent period of challenge".
However, it said the terms of reference would be "critical to the success or otherwise of the investigation".
The NASUWT also said it will "seek assurances from the panel that their work will not cause any further disruption".
Jim Clarke, chief executive of the Council for Catholic Maintained Schools (CCMS), also welcomed the appointment of the panel.
"The background and experience of those who will be carrying out the investigation gives confidence to the process," he said.
"CCMS will continue with its ongoing work with the other interests through the agreed strategy. It remains focused on the needs and interests of the pupils at the school."
A three-person panel has been appointed to carry out an investigation into De La Salle College in west Belfast.