Mr. Blankfein served in the top positions at Goldman Sachs since 2006. He will be named senior chairman after his departure, a company news release said.
"My job has … allowed me to engage with many of the most impressive business leaders around the world, and I thank them for allowing me to help support their goals and priorities," Mr. Blankfein said in the news release.
Mr. Solomon has served as president and co-chief operating officer since 2016 and previously was global co-head of investment banking.
Patrick Scanlan, a Goldman Sachs spokesman, declined to comment on Mr. Solomon's successor in his current positions.
"Lloyd has been a remarkable leader during an extraordinary period of challenge for Goldman Sachs," said Adebayo O. Ogunlesi, lead director of Goldman Sachs' board of directors, in the release.
"The board has been engaged in a multiyear succession process, and we are confident that David will build off the firm's strong financial, risk management and franchise position," Mr. Ogunlesi said.
Goldman Sachs Group's asset management unit had a total of $1.5 trillion in assets under administration as of June 30.