GREENWICH, CONN., JAN. 31 -- American Brands Inc. will buy E-II Holdings Inc. for about $1.1 billion under terms of a definitive agreement announced today by the two companies.

American Brands said the increased offer of $17.05 a share, up from $13 a share, came after the Chicago-based company divulged strategy plans, internal earnings projections and other private information during weekend meetings. ''Our evaluation of this new information demonstrated that there is substantially more value in E-II than our review of publicly available information had indicated,'' American Brands Chairman William J. Alley said in a prepared statement.

The purchase ended a takeover battle that began Dec. 4 when E-II announced it had acquired a 4.6 percent interest in American Brands, and the Greenwich-based company countered with a stock buyback of 10 million shares.

In subsequent days, American Brands enacted a ''poison-pill'' defense to stymie acquisition efforts. Later, American Brands began its successful ''Pac Man'' defense, in which a company attempts to acquire a firm that is chasing it. The strategy was last used in 1982 in a takeover battle involving Bendix Corp. and Bethesda-based Martin Marietta Corp.

The board of directors of E-II, a publicly traded company formed out of Beatrice Cos. last July, on Thursday had recommended to its stockholders that they reject a surprise $13-a-share offer made by American Brands on Jan. 21.

American Brands said it will combine E-II's home fashions, Waterloo, Aristokraft and Twentieth Century's units with its Masterlock and Dexterlock businesses to create a new core business in hardware and houseware products. It said it would also combine E-II's Day-Timers unit with its own office product businesses.