Backs coach Baber and forwards coach Burnell have been asked to lead the Welsh region following the resignation of Dai Young, who joined Wasps last week.
One of their first decisions has been to re-appoint Paul Tito as the captain for a fourth successive season.
Blues chief executive Robert Norster insists the promotion of Baber and Burnell has the backing of the players.
"It has been decided that Justin and Gareth are to be given the opportunity to manage team affairs with the position being reviewed following the World Cup," he said.
"It is a great opportunity for two young aspiring Welsh coaches to put their plans forward and gain greater experience.
"It's a move that's supported by the playing squad who have already been pro-actively engaged in the scheduling of the season's preparations.
"The very nature of the professional game for any individual or team is the management of change and recent events have created for us opportunities as well as challenges that we must all rise to meet."
The Blues reiterated their claim to compensation from Wasps for Young's departure and their willingness to pursue the matter in court.
"While understanding such role changes will rarely be seamless, we very much hope that Dai and his new employers will eventually recognise the need to respect and address the existing contractual position with Cardiff Blues," said Norster.
"It is of course disappointing for all parties that events now appear to be taking a legal course which will prevent further comment at this time."
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