The Scots actor studied drama at the conservatoire from 1988 to 1991, when it was known as the Royal Scottish Academy of Music and Drama.
Tennant, who portrayed the 10th Doctor, will be awarded an honorary drama doctorate at a ceremony this summer.
Renowned choreographer Sir Matthew Bourne and distinguished cellist Ralph Kirshbaum will also be honoured.
Sir Matthew will receive the same honorary doctorate for dance and Kirshbaum for music.
Conservatoire principal Professor Jeffrey Sharkey said: "I am delighted that the Royal Conservatoire of Scotland is to confer honorary degrees on these truly world-class and inspirational individuals.
"They represent the highest levels of artistry in their chosen disciplines and help promote international reach of the performing arts.
"It is fitting that such respected artists join the RCS family in the year that we are named in the world's top 10 for performing arts education."
Professor Sharkey added: "We want to celebrate the exceptional achievements of David, Sir Matthew and Ralph, and the profound impact they have on individuals and audiences around the world."
The honorary degrees will be awarded at a graduation ceremony on 5 July.
Doctor Who star David Tennant is to be awarded an honorary degree from the Royal Conservatoire of Scotland (RCS).