Jacobs will become the 175-year-old firm's executive chairman, focusing on client relationships.
Orszag, who joined Lazard in 2016, currently leads its financial advisory business overseeing deals.
When he takes the reins, Orszag will eliminate that role and reassign his duties to others across the firm, he said in letter to its more than 3,400 employees, calling on them to turn the bank into the "go-to destination" in finance.
"We should aim higher," he wrote.
Lazard was ranked No. 7 in the list of top deal advisers for the first quarter, up from No. 9 last year, according to Refinitiv.
It is the latest Wall Street firm to set out leadership changes. Last week, Morgan Stanley (MS.N) CEO James Gorman said he would step down within a year and become executive chairman, with three candidates in the running to succeed him.
By contrast, JPMorgan Chase & Co's (JPM.N) chief Jamie Dimon said he had no plans to leave the largest U.S. lender after running it for 17 years.
The leadership change comes in a tough year for dealmaking amid economic uncertainty. Lazard reported a surprise loss in the first quarter as activity slumped. Jacobs warned in April of an uncertain outlook for the rest of the year and announced plans to cut about 10% of the company's workforce.
Most recently, Orszag advised First Republic Bank before the lender was seized by regulators and sold to JPMorgan earlier this month.
Orszag was formerly a vice chairman at Citigroup Inc (C.N). He also served in the Obama administration as director of the Office of Management and Budget, and before that, as the director of the Congressional Budget Office.
In recent months, he has represented Lazard at industry conferences and in media interviews.
The executive has a degree in economics from Princeton University and a Ph.D. in economics from the London School of Economics.
"Peter has proven to be a strategic, visionary and decisive leader, with deep relationships across the industry," said Richard Parsons, the bank's lead independent director who previously served as Time Warner CEO and Citigroup chairman.
Orszag has the "ability to effectively lead Lazard through evolving global markets and complex geopolitical dynamics," Parsons said.
