Jil Teichmann had earlier prevailed 6-3 4-6 6-3 over Storm Sanders in a thrilling contest to put Switzerland ahead before Olympic champion Bencic saw off Tomjlanovic 6-2 6-1 to clinch the tie.
The teams also clashed in the semi-finals of last year's event in Prague, where Teichmann overcame Sanders and Bencic defeated Tomljanovic before Switzerland went on to finish runners-up to Russia.
"What happened last year gave us extra motivation," Bencic said in an on-court interview. "We were so heartbroken, I don't think I have ever cried so much.
"But in the locker room Jil came to me and said: 'Next year, we're going to do it, we're going to take it.' And we did, I'm so incredibly proud."
World number 12 Bencic had not dropped a set all week and extended her run against Tomljanovic, delivering a commanding performance to wrap up victory in an hour and 15 minutes.
In a brilliant battle between two left-handers, Teichmann dominated the first set but Sanders, struggling with a leg injury and needing courtside treatment, twice rallied from a break down in the second in a stirring revival.
A fatigued Sanders, who had won all three of her previous singles matches this week, gifted Teichmann the key break for 3-2 in a game that lasted 11 minutes before the Swiss saw out a hard-fought victory in two hours and 18 minutes.
Seven-times winners Australia had beaten hosts Britain in the semi-final and were seeking their first title since 1974. They had also missed out in 2019, when they were beaten by France in Perth.
Australia had replaced the Russian team in this year's competition after the country was banned from defending its Davis Cup and Billie Jean King Cup titles following its Feb. 24 invasion of Ukraine.
Switzerland became the 12th different country to win the tournament, formerly known as the Fed Cup, and the first new champions since Italy in 2006. They also finished runners-up to Spain in 1998.
Victories for Teichmann and Bencic capped a near-perfect tournament for Switzerland as they finished with a 9-1 record in Glasgow, with their only loss coming in the doubles rubber against Canada in Group A.
"We didn't win this just today -- it was this week, it was actually over years, we tried to get better and better at it," Switzerland captain Heinz Guenthardt said.
"You saw how many close points there were, who knows why we win some and lose some. A lot of it has to do with heart, and this team has a lot of heart."
