Coming out publically was "one of the most important decisions" of my life, said Mundell, Scotland Secretary and MP for Dumfriesshire, Clydesdale and Tweeddale.
"The Prime Minister is pleased. Delighted that he's in a position to take this step," a Downing Street spokesperson for David Cameron said.
Mundell made the announcement as part of a New Year message on his website and Facebook.
"New Year, new start! I have already set out my political priorities for the year and now I am setting out my personal one.
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"Over time, I came to understand that, for me, the only way to be truly happy on a personal level is to acknowledge in public as well as in private, who I am. Gender and sexuality should make no difference whether you are a Cabinet Minister or in any other walk of life and I hope that I can, in my own way, reinforce that message," he added.
Lord Smith was the UK's first openly gay Cabinet minister during Labour leader Tony Blair's time as Prime Minister from 1997 to 2007.