The couple wed in scenic Big Sur, California on September 29.
They were seen departing Los Angeles International Airport on October 3 with bags packed for Europe, according to People magazine.
Anne, 29, and Adam, 31, reportedly spent the last two-and-a-half weeks enjoying their first days as a married couple on the romantic getaway.
UsWeekly reports the pair first jet to London before heading to Paris, and later Morocco.
The trip follows the couple's romantic nuptials in coastal California.
The pair invited over 100 guests to the ceremony, which saw Anne walk down the aisle in a custom white lace Valentino gown and floor-sweeping veil.
The couple have been together around four years and were engaged in November.
"I am very much in love with him, [only] Adam totally ruined my plan," Anne said last year. "I was really actually looking forward to a little alone time, and then I fell in love like a fool!"