Eisenberg, who is 37, begins his three-year term this month. He replaces Bob Jones, who is returning to fee earning in the corporate department after a single term in the job.
The election, which took place on Monday, was contested but Jones did not stand for re-election. Eisenberg is a partner in the corporate department. He qualified in South Africa and joined Berwin Leighton in 1989, becoming a partner in 1995.
Peter Robinson, chairman of the firm, says: "In choosing Neville, partners have voted for a partner of vision and determination.