The eighth seed beat the Czech 6-3, 6-7 (1/7), 7-6 (7/3), 7-6 (7/4) in three hours 31 minutes and will play either Rafael Nadal or fellow Swiss Roger Federer in Sunday's final.
Wawrinka, who upset three-time defending champion Novak Djokovic in the quarterfinals, will supplant Federer as the Swiss number one unless the 17-time Grand Slam champion wins the title.
Federer, who has held the top Swiss ranking since 2001, faces off against number one Nadal in the other semifinal on Friday.
This competition marks the first time two Swiss players have competed in the semifinals of a Grand Slam tournament.
The possibility that Wawrinka and Federer could meet in the final has fired people's imaginations in Switzerland.
Earlier this month, the modest Lausanne native was voted Swiss person on the year for 2013 following the best year of his career, although he failed to win any of the major tournaments.
He got off to a strong start this year by winning the Chennai Open in India for the second time.
After his victory against Berdych he credited his improved performances to the help he has been receiving from new coach Magnus Norman.
"I'm speechless, it's amazing," Wawrinka said.
"I am so happy to win that match to make my first final here," he said.
"I am working every day to try and win matches.
"I didn't expect to make a final in a Grand Slam and tonight it's happened, so tonight I'm really happy."
Wawrinka didn't lose serve and only had one break point against him as big-serving Berdych dished up seven double faults, four of them, crucially, in the third and fourth set tiebreakers.
Berdych's serve was only broken once and Wawrinka shaded the Czech by just one point (143-142) throughout the whole match.
It will be Wawrinka's first major final after he lost to Djokovic in five sets in the semifinals at last year's US Open.
Wawrinka reaches a major final at his 36th Grand Slam appearance, and becomes only the second Swiss man behind Federer to play in a slam final.
It was Wawrinka's fourth straight victory over Berdych and his second win over the Czech in three Slams.
Wawrinka won the opening set when Berdych missed an overhead smash on break point in the seventh game, but the Czech levelled the match by taking the second-set tiebreaker.
Both players were unable to break serve and the semifinal was decided with Wawrinka winning the final two tiebreakers to edge home.
Wawrinka hit 18 aces among his haul of 57 winners and won 82 percent of his first-serve points, the same as Berdych.