Virginia M. Rometty, a senior vice president at I.B.M., will be the company’s next chief executive, the directors announced on Tuesday. She will succeed Samuel J. Palmisano, 60, who will remain as chairman, at the start of next year.

Ms. Rometty, 54, is well known within the technology industry, but not widely beyond. She has led strategically important divisions of the company as it has shifted to services and products with high profit margins, like software that mines vast troves of corporate and online data for sales and cost-saving opportunities.

The directors’ choice of Ms. Rometty, who managed a crucial merger as well as sales in fast-growing new markets, ends a competition that has been under way for years. The leading candidates were always from within the company’s executive ranks.

A leading rival to succeed Mr. Palmisano, analysts say, was Steven A. Mills, the senior vice president who led I.B.M.’s highly profitable and growing software division. But his age, analysts note, was probably an obstacle. Mr. Mills has just turned 60, the traditional retirement age for I.B.M. chief executives.