The White House has been preparing for months for a smooth handover of power to the new president in January, and on Friday, Denis McDonough, President Obama’s chief of staff, called Mr. Meier, one of Mrs. Clinton’s policy aides, and Mr. Christie to discuss the next steps in the process.

During the calls, said Brandi Hoffine, a White House spokeswoman, Mr. McDonough invited representatives of both campaigns to begin attending transition-planning meetings and told them their campaigns could now arrange for intelligence briefings through the Office of the Director of National Intelligence.

Mr. McDonough also told both campaigns that they were eligible to begin using office space in a Pennsylvania Avenue building a block from the White House, provided by the General Services Administration, to begin coordinating their transition planning.

A top White House official met in April with representatives of several presidential campaigns, including Mrs. Clinton’s and Mr. Trump’s, at a gathering at Kykuit, the estate built by John D. Rockefeller in New York’s Hudson Valley, to begin discussing transition preparations. Mr. McDonough convened the Cabinet in March to begin the administration’s transition planning, and both a White House Task Force and an agency transition committee began meetings in June to begin preparations.

Mr. Obama has told his top advisers that he benefited greatly from the transition process organized by President George W. Bush in 2008.