Baker and Ward will both play singles in the Euro/Africa Zone Group I second round clash with Colin Fleming, who represented Team GB at the London 2012 Olympics, teaming up with Jonny Marray in the doubles.
Marray is the reigning Wimbledon doubles champion having won the title with Danish partner Frederik Nielsen last year while Baker reach the main draw of the Australian Open in January.
Baker last played in the Davis Cup during Britain's defeat of Tunisia in Group II two years ago while Ward suffered a broken wrist last year but is now back.
If Britain defeat Russia they will go forward to the World Group play-offs in September but if they lose they will face a Group II relegation play-off at that time of year instead.
And, while aware of the size of the task in hand against Russia, Smith admitted his satisfaction at the make-up of his squad with Baker and Ward back in action.
Andy Murray will miss out as he prepares for the French Open and Smith said: "It's great to have Jamie Baker back in the team after him starting the year so well in qualifying at Australian Open in January.
"James Ward has done fantastically well to come back from a long-term injury sustained last year and brings a lot of Davis Cup experience to the team having played in six of the last seven ties for his country.
"Colin Fleming has had a great start to 2013 winning ATP titles in both Auckland and Marseille. In Jonny Marray we have the current Wimbledon doubles champion who also went on to reach the semi-finals of the ATP World Tour Finals at the end of last year.
"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."