NEW YORK - Allstate, the largest publicly-traded auto and home insurer, said on Tuesday that it had picked AIG executive Matthew Winter to be the chief executive of its troubled life insurance division.

Winter, a vice-chairman at American International Group Inc, will leave AIG effective Oct. 19, according to an internal AIG memo dated Oct. 6 and obtained by Reuters.

He had been named vice chairman of transition planning and administration at AIG just last April in addition to serving as chief executive of American General Life Cos, the large U.S. life insurance unit of AIG.

Winter's departure is another in a steady stream of AIG defections to competitors in recent months, following last year's bailout by the federal government.

At Allstate, Winter, 52, will lead the company's life insurance and retirement products division, effective Oct. 26, according to a company statement.

Allstate Financial, which provides life insurance, supplemental accident and health insurance, annuity, banking and retirement products, had been seeking a unit CEO since early in the year, when James Hohmann left.

Allstate CEO Tom Wilson had said the unit needed a shakeup, after the business sustained large losses.

We must be more focused on creating a sustainable business model that reflects a new economic environment and reality for our customers, Wilson told investors in late 2008, promising significant job and expense cuts at the unit.

Until a successor is named to replace Winter at AIG, those who reported to him will report directly to AIG CEO Robert Benmosche, said the memo signed by Benmosche.

Benmosche is the fourth chief executive at AIG since June last year.

He is overseeing a broad restructuring and trying to pay down more than $80 billion in outstanding federal loans that were extended to help AIG cover guarantees it sold on mortgage-back securities that plummeted in value. (Reporting by Lilla Zuill; Editing by Tim Dobbyn)