"We all four felt that, after some 35 years, it could be fun to join forces again and go into the recording studio. So we did," the group said in a statement after repeatedly vowing they would never reunite.
The new songs "I Still Have Faith In You" and "Don't Shut Me Down" were recorded last summer, the band's manager Gorel Hanser told TT news agency.
The quartet split up in 1982 after dominating the disco scene for more than a decade with hits like "Waterloo", "Dancing Queen", "Mamma Mia" and "Super Trouper".
"It was like time had stood still and that we only had been away on a short holiday. An extremely joyful experience!" members Agnetha Faltskog, Bjorn Ulvaeus, Anni-Frid Lyngstad and Benny Andersson added.
The group, which sold more than 400 million albums, have not sung together publicly since 1986.
"I think it's going to sound pretty much like their last songs from 1982, with quite a mild tempo, not like 'Voulez-Vous' or 'Gimme Gimme Gimme'," Carl Magnus Palm, who has written several books about the group, told AFP.
"Frida's and Agnetha's voices are the same, so it won't be a huge difference," he said.
Palm said he was stunned by Friday's announcement.
"I'm as surprised as everyone else.... They've always been so adamant that they weren't going to make new music."
The news came as Sweden mourned the death of another of its music sensations, Avicii, one of the world's most successful DJs whose real name was Tim Bergling.
He was found dead a week ago in Oman where he had been on holiday with friends.
'Come of age'
Computerised avatars are to perform "I Still Have Faith In You" in a TV special produced by NBC and the BBC to be broadcast in December, the group said.
Bjorn, 73, was married to Agnetha, 68, and Benny, 71, was married to Anni-Frid, 72.
The group dominated the 1970s disco scene with their glitzy costumes, kitsch dance routines and catchy melodies.
While they have appeared in public together on rare occasions, they have never reunited to perform as a group, and have vowed that won't ever happen.
"There is simply no motivation to regroup. Money is not a factor and we would like people to remember us as we were," Ulvaeus said in a 2008 interview.
Friday's announcement elicited as much joy as shock among observers.
Richard Skold, a 46-year-old ABBA fan who works at a Stockholm book store, jumped up with surprise after hearing the news.
"This is the craziest thing I've heard! I never thought this would happen. And the fact that they're all still alive is fantastic!" he told AFP.
"BREAKING: ABBA have reformed. This may be bigger than Korea," British journalist and TV personality Piers Morgan tweeted, referring to Friday's historic meeting between North Korean leader Kim Jong Un and the South's President Moon Jae-in.
'The same wonderful chemistry'
The group's manager Gorel Hanser told TT that hearing the four record the two new songs was "just like in the ABBA days".
"It was the same wonderful chemistry. It was as if time had stood still," Hanser said.
"Everyone got into their role and sang, and sang and sang," she said, adding the band was not planning to tour together in real life.
Their popularity has continued to grow over the years, with the 1999 hit musical "Mamma Mia" and the 2008 film of the same name starring Meryl Streep bringing their music to a whole new generation of fans.
ABBA's music also featured prominently in two cult Australian films, "The Adventures of Priscilla, Queen of the Desert" and "Muriel's Wedding", both released in 1994.
In 2013, the world's first museum dedicated to ABBA opened in Stockholm, offering visitors a chance to get up close and personal with the foursome with a little help from modern technology.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.