Last month, Goldman’s board met at its headquarters and evaluated the two candidates. Mr. Blankfein offered his view, and the directors decided that Mr. Solomon was their man, according to a person who was briefed on the meeting.

The anticipated elevation of Mr. Solomon, a Goldman veteran who moonlights under the name D.J. D-Sol, spinning electronic-dance music, marks a strategic shift for the bank.

Mr. Solomon, a native of Westchester County, N.Y., was a rare outsider to join Goldman as a partner when he was hired from Bear Stearns in 1999. He is a schmoozer who recognizes the importance of projecting a positive, inclusive image of the bank to its clients, its employees and the public. Unlike Mr. Blankfein and Mr. Schwartz, Mr. Solomon is not steeped in the firm’s cutthroat trading culture.

“He’s client-centric, direct and candid,” Bennett Goodman, a senior managing director of the private-equity firm Blackstone, said in an email. “You never doubt he’ll tell you what he really believes even when it’s not what you want to hear.”

The leadership transition comes at a time when Goldman’s traditional business model is under siege. Its bond-trading business, once a huge component of the firm’s revenue, which hit nearly $1 billion a week in 2009, is now a shadow of its former self. The bank’s limited presence in countries like Saudi Arabia and Mexico has meant Goldman has been left out of some lucrative transactions. And its belated attempts to muscle its way into businesses such as consumer lending have failed to transform the company into a real competitor of commercial banks like JPMorgan Chase and Citigroup.

Since his elevation to president was announced in late 2016, Mr. Solomon has been working to address those shortcomings. Last spring, he and Mr. Schwartz presented directors with a plan to generate $5 billion a year in additional revenue starting in the fall of 2020. It called for expanding Goldman’s investment-banking franchise to midsize cities including Dallas and Seattle.

At the same time, Mr. Solomon strayed beyond the traditional mold of a Wall Street power broker. He demanded, for example, that Goldman’s recruiters increase their hiring of women with the goal of eventually reaching total gender parity.