Baker comes into the team after a great qualifying run at the Australian Open earlier this year, and Ward is returning to form after a long term injury.
Fleming and Marray have been playing together on the tour, and Marray has just returned to the partnership after a calf injury earlier this year.
Smith said: “We look forward to the challenge of competing against a very strong Russian side and, with the advantage of a home crowd supporting the team, we hope we can make life as difficult as possible for the opposition.”
The last time GB and Russia met each other in the Davis cup was 1963, with the Brits victorious (4-1) at Devonshire Park, Eastbourne.
The winners of this tie will be drawn on April 10 to compete in the 16-nation World Group Play-offs from September 13-15.
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