The tie, taking place on Sept. 18-20, will be held indoors at the city's Emirates Arena.
"It's exciting for the team to be going back to Glasgow," Scot Murray, the world number three currently in action in Montreal, said in a statement from British Tennis.
"It's always special to play in front of a home crowd.
"We are fortunate to have played our last three ties at home. We had a unique atmosphere in Glasgow, the crowd was unbelievable. It's going to be a huge week for our team."
Murray, who can expect deafening support, has a superb record for Britain in Davis Cup singles matches, winning 21 of 23.
The venue was used for the World Group first round tie in March when Britain beat the United States.
Britain are bidding to reach the final for the first time since 1978. They last won the team event in 1936.
The other semi-final is between Belgium and Argentina in Brussels.
(Editing by Martyn Herman)
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