The team will comprise of Wimbledon and US Open champion Andy Murray, Dan Evans, James Ward and Colin Fleming.
The winners of this tie will advance to the elite 16-nation Davis Cup by BNP Paribas World Group. The last time Britain took part in the World Group was 2008.
Leon Smith said: “We are delighted to be sending our strongest possible team to Umag in what will be a very tough tie.
"Croatia are former winners of the Davis Cup and currently ranked No. 11 in the world, but as we proved in Coventry back in April, we can upset the odds. May the best team win promotion into the World Group.”
Adrian Grace, CEO Aegon UK, said: “We’ve been enjoying some excellent British performances in both the men’s singles and doubles at the US Open. It is very encouraging to see such a strong Aegon GB Davis Cup Team named for this extremely important tie against Croatia.
!As sponsors of the British Davis Cup team since 2009 we’re looking forward to our first experience of a World Group play-off match. We wish Leon Smith and the team every success.”
The tie will be broadcast live each day by British Eurosport. Matches commence at 10am British time Friday and Sunday, while the doubles on Saturday will be at 1pm British time.