The draw saw Leon Smith’s side dealt a first away tie in more than three years as they look to return to the elite 16-team World Group for the first time since 2008.
Croatia's team is headlined by world number 11 Marin Cilic while Ivan Dodig, ranked 54, is also expected to feature in the match to take place between September 13 and 15.
Croatia have competed in the World Group for 11 of the last 12 years and have won four of their last five World Group play-offs.
But they find themselves in a relegation scrap after losing 3-2 to Italy in the first round in February as Dodig lost all three of his matches, including partnering Cilic in the doubles.
Britain were not one of the eight seeded nations in the draw as they are currently ranked 30th in the ITF Davis Cup nations rankings which is based on recent performances.
Andy Murray has confirmed he will return to Davis Cup action after a two-year absence for the tie.
Murray missed both of the nation's ties in 2012 and the dramatic clash with Russia in the Europe/African Zone Group I play-off last weekend.
World number 325 Dan Evans and 217 James Ward won in Coventry on Sunday to complete a first victory from two rubbers down for Britain in 83 years.
The match, at an unconfirmed venue, will take place only five days after the US Open final which Murray will hope to be involved in as he seeks to defend his maiden Grand Slam title.
When Scot Smith took over from John Lloyd in 2010, Britain had suffered consecutive relegations from the World Group to Europe/Africa Zone Group II.
His first task was a relegation play-off against Turkey to avoid going down to Group III - and Britain survived. Smith oversaw a return to Group I and now hopes to make it two promotions in three years.
Smith will look to Murray and the doubles pairing of Jonathan Marray and Colin Fleming, ranked 16 and 28 respectively, to give GB the three wins required for victory.
Britain are the third most successful team in Davis Cup history, having won nine titles, but have only appeared in one final since 1937.
Poland v Australia
Germany v Brazil
Switzerland v Ecuador
Croatia v Great Britain
Netherlands v Austria
Spain v Ukraine
Belgium v Israel
Japan v Colombia
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