Carphone Warehouse, which provides broadband under its TalkTalk brand, will take on Tiscali's 1.45m UK broadband and 300,000 dial-up customers.
The deal, still subject to EU competition clearance, is expected to be completed by June.
With the agreement TalkTalk becomes the UK's largest resident broadband provider and second overall behind BT, with 4.25m customers and a 25% market share.
Carphone Warehouse intends to merge the Tiscali business with its TalkTalk brand, although customers will be able to keep their Tiscali email addresses.
Charles Dunstone, Carphone Warehouse CEO, said the deal provides significant shareholder value and will boost 2009's earnings per share.
Mary Turner, Tiscali CEO, called the agreement "good news" for its customers.
Turner said: "The combination of TalkTalk and Tiscali will offer our customers, both residential and business, Britain's largest and best fully unbundled network.
"The enlarged TalkTalk is perfectly positioned to meet and anticipate these demands."
The agreement comes 18 months after Tiscali first set out to sell its UK business. The £236m price is less than half the £550m bid Carphone Warehouse made last year, which was rejected by Tiscali.
Tiscali's initial valuation of £1.3bn was quickly whittled away by the deteriorating economy, steady losses in its 1.8m UK customer base, and Tiscali's declining share price.
In December, BSkyB, which also expressed interest in the company, scaled back its £450m bid and eventually walked away from the offer in April.
Vodafone, BT, Swisscom and Italian mobile network Wind also considered buying Tiscali's UK business.
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