“Republicans have suffered from being behind in small-dollar fund-raising, and the president, over the course of the campaign and his presidency, has built the largest Republican first-party data list,” said Mr. Trump’s campaign manager Brad Parscale, who engineered the agreement. “So giving other candidates and groups access to that data through a legal means to rent it was one of the best things I could do for the Republican ecosystem. And the campaign makes a little money, too. It’s a win-win.”

So far, parts of the list have been rented to a number of Republican candidates — including the gubernatorial campaign of Ron DeSantis in Florida and the Senate campaign of Josh Hawley in Missouri — as well as nonprofit groups advocating the confirmation of Brett M. Kavanaugh to the Supreme Court, and even to an author promoting a pro-Trump book, according to people familiar with the arrangement.

Digital files of supporters’ data have become indispensable tools of modern campaigns, relied upon for fund-raising, mobilizing volunteers and rallying supporters to get out to vote. And they have become valuable currency in their own right, sometimes reaping millions of dollars in rental fees for the campaigns that built the lists and the list brokers who arrange the rentals.

It is not uncommon for former candidates to rent or sell their lists to pay down debts, or for active campaigns to swap parts of their lists with those of ideologically aligned party or campaign committees to build their networks.

The Trump campaign maintains ownership of the list as well as veto authority over all rentals, according to interviews and the marketing emails. One such email indicates that “as long as the political group, org, nonprofit or business is not hostile to the president, then they are most likely able to use the data with no problem.”

It is not clear whether the president, who is known to abhor the prospect of others’ profiting from their affiliations with him, is aware of the details of the arrangement.

The people familiar with the arrangement said that the rentals so far had been sparing, but that the volume began increasing in recent weeks as key midterm races began heating up.