The trip to the United States is reward for the 4-1 win over Croatia at the weekend which ensured Great Britain were back in the elite World Group for the first time since 2008.
The tie, which is the 18th to be played between the two countries, is set to be played between January 31 and February 2 with the location and surface to be announced at a later date.
It will be the first time the teams have met in the competition since 1999 when the United States triumphed in a thrilling clash in Birmingham and is a rematch of the first ever Davis Cup tie.
Then, the United States took a 2-0 lead through Todd Martin and Jim Courier before Tim Henman and Greg Rusedski pulled one back in the doubles and then the former levelled the tie with victory over Martin.
It all came down to the decisive final rubber which pitted Courier against Rusedski, only for the American to triumph 8-6 in the fifth set.
Smith recalled this on the Lawn Tennis Association's Twitter: "It is an exciting tie in prospect with fans remembering the great drama when the nations last met.
"We'll go into the tie with a lot of confidence and look forward to it."
Great Britain could have faced a more difficult tie with the likes of reigning champions Czech Republic and their 2013 final opponents Serbia lurking in the draw alongside Spain.
The USA were seeded sixth of eight teams but still present tough enough opponents with John Isner and Sam Querrey world ranked 15th and 31st respectively while Bob and Mike Bryan are the worlds top-ranked doubles team.
While world number three Andy Murray has committed himself to the GB cause, there are no other British players in the top 100.
British number two Dan Evans has been improving and won the final, dead, rubber against Croatia but he is ranked 152 in the world with James Ward at 179.
The Wimbledon champion may well find he is in for a grueling tie against a team captained by Courier if the Croatia clash is anything to go by, the Scot having teamed up with Colin Fleming in the doubles.
Minutes before the draw took place, Smith told the Davis Cup live stream on www.daviscup.com: "It's been really good and a great journey for the past three and a half years.
"But I think I can speak on behalf of the players and the staff that this tournament is like no other.
"The great thing about the Davis Cup is that it's a team effort which requires everyone to play their part.
"When we faced Russia in April we were classed as the underdog but Jonny Marray did well and Andy came in for these games and it's been a great team effort.
"It's the most exciting spectacle. Like what we saw in London at the Olympics, it's time for the fans to get behind the team and it's been character building for the players involved."
Regarding Murray's involvement next year, Smith added: "Yeah, he's very committed. The great thing is it's a time to get the players and staff together to work together and have a good time."
Elsewhere in the draw top seeds Czech Republic were drawn to host Holland while Serbia, who are seeded second, will take on Switzerland.
That has set up the prospect of world number one Novak Djokovic meeting Roger Federer.
Third seeds Spain travel to Germany, Canada take on Japan and France will host Australia in the top half of the World Group draw.
In the other half Italy face fourth seeds Argentina and Belgium face a tricky trip to Kazakhstan.