According to the latest DOJ comments, the White House was only informed of Rosenstein's decision to appoint a Special Counsel in the Russian probe after the order was signed. Per Bloomberg:
*WHITE HOUSE TOLD OF MUELLER APPOINTMENT AFTER ORDER SIGNED: DOJ
Courtesy of Bloomberg's Jennifer Jacobs, here is a full breakdown of today's sequence of events:
The Department of Justice has announced the appointment of former FBI Director Robert Mueller as Special Counsel to oversee the federal investigation into Russian interference in the 2016 election, including potential collusion between Trump campaign associates and Russian officials.