It’s the first time Great Britain has made this stage of the competition since 1981, where they will face Australia.
Murray beat Gilles Simon 4-6, 7-6, 6-3, 6-0 to secure a 3-1 victory against France.
After beating Jo-Wilfried Tsonga in his first match and alongside brother Jamie in the doubles saw off Nicolas Mahut and Tsonga, Murray scored three points for his team.
Against Simon, Murray trailed a set and 4-2, before engineering a comeback.
“Obviously it feels good to get through that,” he says.
“It wasn’t looking great in the second set, but I used up my last ounces of energy.
“I just tried to change my tactics.
“Gilles was playing so solid, so I said ‘Chase every ball’.
“I didn’t care how I played, I just wanted to win and that’s what I did.”
Murray endorses the HEAD Graphene Radical racquet.