GB will host the 2006 champions from April 5-7 at an unconfirmed venue.
If Leon Smith's men win then they will get a shot at a return to the World Group for the first time since 2002 in September.
They were the only one of the seven unseeded nations to be given a first-round bye when the draw was held in London.
Mikhail Youzhny at 25 is the top ranked player for Russia, who were relegated from the World Group this year, while veteran Nikolay Davydenko is also in the top 50.
Defending champions Spain, who face Czech Republic in this year’s final, have been handed an away tie against Canada in the World Group first round.
The Czechs face a trip to Roger Federer's Switzerland.
Canada v Spain
Italy v Croatia
Belgium V Serbia
USA v Brazil
France v Israel
Argentina v Germany
Kazakhstan v Austria
Switzerland v Czech Republic
Europe/Africa Zone Group I:
Poland v Slovenia
Finland or Denmark v Romania
Ukraine v Slovak Republic
Bye: Russia, Great Britain, South Africa, Sweden, Netherlands
Great Britain v Russia