The 19-year-old has been preferred to British number two Dan Evans in the team to take on the United States at Petco Park baseball stadium in San Diego next weekend.
Edmund joins Andy Murray, James Ward and doubles specialist Colin Fleming for Britain's first World Group tie in six years.
Edmund is ranked 372nd in the world - 222 places below Evans - and is only the British number eight, but he is highly regarded by everyone in British tennis.
He joined Murray at his winter training camp in Miami last month and has been invited back in March.
The fact the tie will be played on clay also works in Edmund's favour, with nearly all his senior tennis so far coming on the surface.
He won a title on clay on Sunday in Florida but that was at a Futures tournament, the lowest rung of professional tennis. The patriotic fervour of a Davis Cup tie will be something quite different.
Smith insists he has not yet chosen between Edmund and British number three Ward, although he has a "gut feeling".
The Scot told Press Association Sport: "Both James and Kyle are very much in the frame and if it is Kyle then I've got no fears about him playing in that environment.
"He's got the game and I think he's ready to move up quickly this year. He's put in the hard work to be able to play best of five sets on clay.
"You look at the impression that (Australian teenagers) Nick Kyrgios and Thanasi Kokkinakis made at the Australian Open. With these young guys it's about giving them opportunities and the best ones take them and show the world what they can do. Kyle can do that."
Clay is certainly Evans' weakest surface but the 23-year-old did not help his cause with a poor performance in front of Smith to lose in the second round of qualifying at the Australian Open.
Evans then chose to go home rather than travel with Ward to Hawaii for a Challenger tournament, which had been Smith's plan.
The captain said: "Had this tie been on a fast indoor hard court then he would have been the first name on the teamsheet after Andy, no question.
"It's a shame that Dan thought he couldn't go to Hawaii but he had his reasons, it was his choice. He'll certainly be in the frame for the next tie."
In an apparent reference to his omission from the team, Evans wrote on Twitter: "Gut feeling normally is the right feeling!"
Smith has also left himself options for the doubles rubber, although his first-choice pairing would almost certainly be Murray and Fleming.
Dominic Inglot, the highest-ranked British doubles player, has been called up for the first time as reserve but there was no place for either Jamie Murray or Ross Hutchins.
Hutchins is back playing with Fleming after recovering from cancer and had hoped to be selected.
Smith said: "They played really well at the Australian Open and, when fit, Colin and Ross are a pretty strong partnership.
"I felt it was a little bit early for Ross. It's different playing on clay, it's different playing best of five sets and it's different playing the Bryans."
Britain certainly go into the tie as underdogs despite Murray's presence, with United States captain Jim Courier selecting his strongest team of John Isner, Sam Querrey and world number one doubles team Bob and Mike Bryan.
It was 1986 when Britain last won a World Group tie in the competition, but Smith believes his side have what it takes.
"We've had some great players in the last 28 years," he said. "Tim (Henman) and Greg (Rusedski) had some amazing ties but they couldn't quite win one.
"This tie is equally difficult. The Americans don't have a grand slam winner but they have John Isner, whose record in Davis Cup last year was superb, especially on clay. And the Bryans are the best doubles team in the world.
"But with Andy in our team we have a chance against anybody. It would be absolutely brilliant if this could be the tie that we won after so many years."