The purchase will also put Tiscali in fourth place as a provider of internet services in the UK.
Tiscali is paying 100m euros (£62m) for the ISP, which is a joint venture between British Telecom and United Business Media.
The purchase will also put Tiscali in fourth place as a provider of internet services in the UK.
The deal values LineOne well below estimates at the height of the internet boom when the company was once considering a £1bn float on the stock market.
Acquisition trail
Tiscali has been on a buying spree recently, announcing on Tuesday the purchase of pan-European ISP SurfEU for 69.6m euros.
In January, Tiscali agreed to buy France's Liberty Surf in a deal valued at 645.5 million euros (£408.5m).
A month earlier, the Italian company had clinched the purchase of Dutch rival World Online for 3.4bn euros ($3.04bn).
Number two in Europe
With LineOne, Tiscali will have 16 million registered users in Europe, including seven million active subscribers.
After its acquisition of Liberty Surf, Tiscali became the second largest European ISP, in terms of active subscribers.
The top ISP in Europe is T-Online, which has 8.7 million active subscribers. But Tiscali does have the largest geographical footprint in Europe.
The Italian company said the acquisition would bring closer the point at which it will break even, although it gave no indication of when this would be.
Tiscali said it aims to become one of the top three ISPs in all of the European countries it has a presence in.
ISP consolidation
LineOne is the latest UK internet venture to bought up by a foreign company. Last year the ISP Freeserve was bought from the retail chain Dixons by the French company Wanadoo.
Consolidation among ISPs has long been expected as the companies struggle to make money.
LineOne, which has 1.85 million registered subscribers, was put up for sale after United Business Media, formerly United News & Media, decided to focus on business publications and media.
BT is expected to use the proceeds to chip a bit off its debt burden, estimated at £30bn. The UK telecom group also announced on Thursday the appointment of Sir Christopher Bland to replace chairman Sir Iain Vallance.
Tiscali is paying 80% the 100m euro price tag with new Tiscali stock. The remainder will be paid in cash.
LineOne is also known as Springboard Internet Services.