HASTINGS, Neb.—The Clinton Global Initiative, which arranges donations to help solve the world’s problems, set up a financial commitment that benefited a for-profit company part-owned by people with ties to the Clintons, including a current and a former Democratic official and a close friend of former President Bill Clinton.

The $2 million commitment was placed on the agenda for a September 2010 conference of the Clinton Global Initiative at Mr. Clinton’s urging, according to a document from the period and people familiar...