World number three Wawrinka will open against 64th-ranked Andrey Golubev while Federer, ranked fourth in the world, will then take on 56th-ranked Mikhaïl Kukushkin.
The Swiss pair, winners of the Olympic doubles title in 2008, will then team up on Saturday for the doubles rubbler against Aleksandr Nedovyesov and Evgeny Korolev.
"Obviously we're favourites," said Federer after Thursday's draw.
"But we're trying to seize our chance," he said.
"It's always an advantage to play at home."
The Swiss can count on a 16,000-strong home crowd over three days of competition.
"It's more than a meeting, it's an event, I think," said Federer.
"There are so many people, we've found a big arena to play in and a lot of tickets have been sold, it's extraordinary," said the former world number one.
The 17-time Grand Slam winner believes Wawrinka's great start to the season by winning the Australian Open has helped draw in the crowds.
"The last six months have been quite extraordinary," said Federer, pointing out that both of them had also reached the semi-finals of the London Masters.
"Now we're both in the top four, it's great," he said.
"It's a great time for Swiss tennis."
The Swiss have only ever reached the Davis Cup final once — in 1992 when they lost to the United States 3-1 in Fort Worth — and Federer would love to add the team title to his honours list, which lacks only that and Olympic singles gold.
Meanwhile, Wawrinka acknowledges that Switzerland has its best chance in years to win a first Davis Cup title.
"We all know that we have a good opportunity, especially since Roger [Federer] is playing and I am playing," Wawrinka said.
"We are not thinking already to the final, but we are, on paper, big favourites for this weekend."
Wawrinka, 29, who has played Davis Cup since 2004, said that although he was now the Swiss number one ahead of 32-year-old Federer, "it does not change who is boss in the team".
Despite all signs pointing to a Swiss victory, Kazakhstan believe in their chances.
"It will be hard to play against them," Kukushkin said.
"We musn't pay any attention to the public, to the 16,000 fans," he said.
"But we have a chance to win, and we'll do everything in our power to achieve this."
Friday from 12:30pm
Stanislas Wawrinka (SUI) v Andrey Golubev (KAZ)
Roger Federer (SUI) v Mikhail Kukushkin (KAZ)
Saturday from 12:30pm
Stanislas Wawrinka (SUI)/Roger Federer (SUI) v Aleksandr Nedovyesov
(KAZ)/Evgeny Korolev (KAZ)
Sunday from 12:30pm
Stanislas Wawrinka (SUI) v Mikhail Kukushkin (KAZ)
Roger Federer (SUI) v Andrey Golubev (KAZ)