A former portfolio manager of New York state’s pension fund steered more than $2 billion in business to two brokerage firms in exchange for bribes that included prostitutes, cocaine, concert tickets and a $17,400 Panerai watch, federal prosecutors said Wednesday.

“This was an age-old and classic tale of quid-pro-quo corruption,” U.S. Attorney Preet Bharara said at a news conference in Manhattan announcing the indictment.

Concerns...