The Golden Globe-winning star of House, Veep, Blackadder and The Night Manager will make a one-off appearance at the EICC on 22 August.
Laurie, who is at the 1200-capacity Pentland Auditorium as part of the Pleasance line-up, is due in the city in August to collect an outstanding achievement award at the Edinburgh TV Festival.
Laurie, 59, is expected to recall how he arrived at the Fringe as an unknown to perform with a group of fellow Cambridge University students, including Emma Thompson, Tony Slattery and Stephen Fry.Their revue, The Cellar Tapes, won the inaugural Perrier Award, which would go on to become the most prestigious comedy prize at the Fringe.
Fry and Laurie formed a hugely-successful comedy partnership in the 1980s and 1990s thanks to shows like Blackadder and Jeeves and Wooster.
He made a number of movie appearances in the likes of Sense and Sensibility, 101 Dalmations, Stuart Little and Maybe before finding fame in America with his role in House, The Manager and Veep.
Fry is also due to make a return to the stage in the city this August in a series of solo shows inspired by Greek mythology, which are part of the Edinburgh International Festival's programme.
Tickets for Laurie's appearance at the EICC are on sale now on the Pleasance website.