The new sign, called Piccadilly Lite, will stand alongside existing advertising for McDonald's, Coca-Cola, Samsung, TDK and Sanyo.
Time slots for personal messages will take up to 10 minutes a day at a rate of £1,000 a minute.
The remaining time will be taken up with brand advertising in two-week, 30-second sequence packages for £7,000.
A website has been launched to mark the initiative, allowing visitors to explore the history behind the site and find out about advertising opportunities.
James Birkett, asset manager for Land Securities' London Portfolio, said: "In order to try out how their messages will look, brand representatives and members of the public will all be able to experiment on an interactive section of the site too -- a real chance to see their message in lights."
Land Securities is a real estate investment trust that owns many landmark buildings such as the Piccadilly Lights and Westminster City Hall, and is developing some of the capital's most innovative mixed-use schemes, such as 20 Fenchurch Street, in the City of London.