Corus chairman Jim Leng said the new terms were a "substantial increase" on Tata's previous offer, and Corus would be recommending the deal to shareholders.
Corus, Europe's second-largest steel maker, has been a takeover target for months. Sunday's announcement pre-empts an offer for Corus that had been expected to be announced next week by Brazil's Companhia Siderurgica Nacional.
Tata chairman Ratan Tata said: "We remain convinced of the compelling strategic rationale of this partnership."
In October, Corus agreed to a takeover bid by Tata that had valued the company at 4.3 billion pounds ($8.4 billion). Siderurgica later said it had approached Corus over a possible higher bid.
Last month, Corus postponed a shareholder vote on the Tata bid until Dec. 20 to give the Brazilians more time to make a formal offer.
Corus shares closed Friday at 500 pence on the London Stock Exchange, equal to the latest offer from Tata.
Corus:
Tata Steel: