Argentina will try to put the failure of past David Cup campaigns behind it when it goes for its first title in its fifth finals appearance against Croatia in November.
The Argentines, who previously lost in the finals in 1981, 2006, 2008 and 2011, got another shot at the trophy after Leonardo Mayer sealed his team's thrilling 3-2 win over defending champion Britain by beating Dan Evans in the deciding match of their semifinal tie on Sunday.
Croatia advanced to the Davis Cup final for only the second time with Marin Cilic's straight-set win over France's Richard Gasquet, which gave his side an unassailable 3-1 lead over the French with one singles rubber left to play.
Argentina is one of four countries, along with Belgium, India and Romania, that has yet to win the Davis Cup after reaching more than one final. The Argentines, however, have been on the losing end in championship rubbers more than anyone else, losing to Spain twice (2008, 2011), Russia (2006) and the United States (1981).
Croatia, which beat Slovakia to win the title in 2005, will host the finals from Nov. 25-27.
In front of a home crowd in Glasgow, Scotland, Andy Murray ensured that Britain's semifinal against Argentina would go to the deciding match when he breezed past Guido Pella in straight sets in the opening singles match on Sunday, 6-3, 6-2, 6-3.
Evans expected to face Juan Martin del Potro, who beat Andy Murray on Friday, in the decider, but the former U.S. Open champion did not want to risk his fragile body after wrist injuries earlier in the year, so Mayer was named as a last-minute substitution.
Mayer, who is ranked 114th, then rallied to defeat the 53rd-ranked Evans 4-6, 6-3, 6-2, 6-4.
"Leo's match was something we believed could happen, but I think it was a great effort from his part after playing a little nervous in the first set," Argentina captain Daniel Orsanic said.
In Zadar, Croatia, Cilic beat Gasquet 6-3, 6-2, 7-5 in the first singles match on Sunday to clinch the tie for the hosts.
Cilic, the 2014 U.S. Open champion, won both of his singles matches and teamed up with Ivan Dodig on Saturday to stun top-ranked doubles pair Nicolas Mahut and Pierre-Hugues Herbert.
Marin Draganja replaced Borna Coric for the meaningless final rubber and lost 6-4, 6-4 to Lucas Pouille.
"We are still pinching ourselves, that's how excited we are with the result," Croatia captain Zelko Krajan said.
Nine-time champion France played without Gael Monfils and Jo-Wilfried Tsonga, who were both ruled out by knee problems.
In other results, Jan-Lennard Struff defeated Hubert Hurkacz 7-6 (4), 6-4, 6-1 to preserve Germany's World Group status with a 3-2 win over Poland in their playoff.
Earlier, Marcin Matkowski upset Florian Mayer 6-2, 4-6, 6-2, 6-3 as Poland came from 2-0 down to level the tie.
Russia is also returning to the top level of the Davis Cup for the first time since 2012 after beating Kazakhstan 3-1.
The schedule was backed up due to rain on Friday, leaving four potential matches to play Sunday. Kazakhstan's Mikhail Kukushkin beat Russia's Evgeny Donskoy to level the tie at 1-1 in the first match of the day, but Russia captured the doubles and then sealed the win when Andrei Kuznetsov beat Kukushkin 6-1, 6-2, 6-2.
A Swiss team lacking stars Roger Federer and Stan Wawrinka came back to defeat Uzbekistan in their World Group playoff 3-2, with 507th-ranked Antoine Bellier securing the final point with a 6-2, 6-4, 6-7 (8), 6-3 win over Jurabek Karimov.
The other teams returning to the World Group next year after winning playoffs this weekend are Spain, Belgium, Australia, Canada and Japan.