The acquisition will see Tiscali's share of the UK broadband market increase to around 15%, overtaking BSkyB to become the third-biggest ISP after Virgin Media and BT, subject to approval from the Office of Fair Trading.
Pipex, which hired David Hasselhoff to front a 2006 advertising campaign, has around a million active customers.
Some 650,000 of these are signed up for its phone package and 570,000 are broadband customers. Around a quarter of a million consumers are signed up to both.
In terms of UK broadband market share, it is seventh-placed, with Tiscali currently in fourth place with 1.4m users.
Pipex had been up for sale since March, and early reports suggested Virgin Media would emerge as a likely buyer. Other rumoured bidders included BT, the Carphone Warehouse and Sky.
The executive chairman of Pipex, Peter Dubens, said: "Tiscali's commitment to investment in [unbundling local telephone exchanges], along with the new TV services it is introducing will offer our existing customers value and choice in the future."
Tiscali estimated it could make cost savings of around £150m by merging the two broadband providers.
The Tiscali UK chief executive, Mary Turner, said: "Significant synergies and efficiencies can be achieved through this acquisition in particular through network integration, customer migration and indirect costs efficiencies."
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