The draw pits Leon Smith's side against familiar foes, with Britain having beaten Kazakhstan and Holland in the same competition in 2019, while their path to the 2015 title began with victory over the USA in the same city.
This time, the US can boast two top-20 players in Taylor Fritz and Reilly Opelka, while Kazakhstan are led by 32nd-ranked Alexander Bublik and the Dutch by another top-40 player in Botic Van De Zandschulp.
Matches will take place at the Emirates Arena from September 14-18 in the week after the US Open, with Bologna, Valencia and Hamburg also hosting groups. The top two teams from each group will then progress to the knock-out stage in Malaga in late November.
The Lawn Tennis Association secured a five-year deal to host group matches - providing Britain are in the last 16 - and has promised to take the event to different cities around the country.
Britain have consistently overachieved in the competition under Smith, reaching at least the quarter-finals in every edition since 2014.
The Russian Tennis Federation won the title in Madrid last year but have been banned from the competition following the invasion of Ukraine, leaving runners-up Croatia as the top seeds.
They will take on Italy, Argentina and Sweden, while there could be a meeting between Rafael Nadal and Novak Djokovic, with Spain and Serbia placed in a high-powered group with Canada and South Korea.
Hamburg, meanwhile, will host matches between Germany, France, Belgium and Australia.