The group, famous for hits including Robert De Niro’s Waiting..., Cruel Summer, Venus and Love In The First Degree, sold 40 million records and last performed together at the Brit Awards in 1988.
But Siobhan Fahey later walked out on her bandmates Sara Dallin and Keren Woodward.
Woodward told Chris Evans’s Radio 2 show: “You just think it’s now or never.
“I gave Siobhan a call, put the idea in her head and thought it was never going to happen, but what do you know, it did.”
Fahey added: “I was really touched because it wasn’t for any other reason that we love each other and we’re really proud of what we did together.
“I was feeling really nostalgic and proud and what a great thing to celebrate.”
The trio have discussed making a new single together but will be touring “all the hits”.
Fahey, who joined Shakespears Sister, told The Guardian that the “feeling of love and friendship had been restored”.
She said of the band’s reputation: “Wherever I go, I’m Siobhan from Bananarama. People wet their knickers when they find that out.”
Tickets for Bananarama’s UK tour go on sale from 9am on Wednesday.