Agnetha, Frida, Benny and Bjorn reunited for the opening night of the concert, which features digital versions of the band.
Frida watched the show with a wide grin across her face, while Benny stood up and clapped along to Dancing Queen.
They took a curtain call at the end, to deafening applause from the audience.
"Abba has never left us, in my heart," singer Agnetha Faltskog told the BBC on the red carpet.
"It was not such a difficult decision [to reunite] because the music is part of us."