Workers used a cherry picker at the weekend to remove the signage at the South Ayrshire airport's terminal.
The slogan is also being removed from marketing materials and branding inside the airport.
It comes as the Scottish Government, which bought the loss-making Ayrshire airport for £1 in November, considers new branding strategies to attract more tourists and business travellers to use to site.
Scotland's transport agency, Transport Scotland, confirmed the slogan had been removed, but there is no information yet on what will replace it.
A spokeswoman said: "As highlighted in the recent statement to Parliament regarding Prestwick's future, we are currently in the process of developing a business plan which includes how we best market the airport and the rich tourist and business offering of Ayrshire and the surrounding area.
"Whilst we have no immediate plans to change the actual name of the airport, branding is clearly a key component. More details will be announced over the coming weeks and months.
"We believe Prestwick can thrive, without harming any of our other airports, and that's very much what the government is focused on."
The reaction to the move on Twitter was overwhelmingly positive, with users commenting that the slogan was the "worst airport branding ever" and "dead on an airport name was never a good idea".
The Scottish Government bought Prestwick Airport from New Zealand owners Infratil to save the site from closure after it failed to find a commercial buyer on the open market.
Ryanair is the only carrier currently using the airport.