The 64-year-old will play the city's Clyde Auditorium on Monday March 18, to mark her 40th year in the music industry.
Olivia announced details of the performances – her first in the UK since the Totally Hot World Tour in 1978 – earlier today.
The British-born Grease star has sold more than 100 million albums.
The 1978 film, co-starring John Travolta, featured such hits as You're The One That I Want and Summer Nights, as well as her solo hit, Hopelessly Devoted To You.
Tickets for the show, which go on sale on Friday at 9am, are available from www.ticketSOUP.com