The tie will take place in the city of Umag on the north west coast of Croatia, starting on Friday 13th September.
Great Britain will be looking to return to the World Group for the first time in five years and may be boosted by the return of the current Wimbledon and US Open champion Andy Murray, who has indicated that he wants to play in the tie.
Without the world number two, Great Britain completed a stunning comeback in April when they recovered from going 0-2 down to beat Russia 3-2 in Coventry. Leon Smith has spoken about Murray's return helping his team to continue the momentum of that win.
Murray played alongside his brother Jamie when the two countries last met in 2007, with Tim Henman completing the team in his last appearance in the tournament.
Despite their loss to Italy in the previous round, the Croatians can call on a strong group of players, with three men in the top 100.
British Eurosport Managing Director David Kerr said, "We are very excited about covering Great Britain's Davis Cup tie against Croatia live and the prospect of watching Leon Smith's team build on their amazing win over Russia.
"There is a lot of talent on both teams and we are assured some great tennis, with the added possibility of Andy Murray's return.
"It completes a strong month of tennis on British Eurosport following as it does our coverage of the US Open."
Lawrence Robertson, Commercial Director of the LTA added, "We're delighted that long-time supporters of British Davis Cup tennis British Eurosport have chosen to cover our forthcoming tie against Croatia. As with all if the previous ties they have covered, they will ensure all British tennis fans will be given the chance to cheer on Leon's team in September"