They are now at sea and "will remain a safe distance from the storm", a spokesperson said in an email.
Carnival Breeze is currently docked in Cozumel and will now overnight there.
The Port of Galveston remains closed to all marine traffic.
The ships packing almost 12,000 guests and roughly 3,700 crew members combined may be delaying returns to the Port of Galveston, a Gulf Coast stop near Houston.
He says utility lines and other infrastructure have been upgraded since 2008 to withstand a Category 5 hurricane.
Both ships would make stops in New Orleans to refuel and resupply and guests would be allow to leave, but would be encouraged to stay aboard and return to Galveston, officials said.
Raikkonen edges Hamilton in FP1 at Spa
It is a race which threatens to be hit by bad weather, but Hamilton, so often a master in the rain, is typically not fazed. Vettel comes out of the annual summer break as the championship leader, with a 14-point margin over his Mercedes AMG rival.
Galveston Port officials said Friday that the cruise ships might not be able to dock in Galveston until Tuesday or Wednesday, but Simons said Saturday afternoon that he was "a little more optimistic".
Although Hurricane Harvey is not expected to hit Galveston head-on, the storm-battered island has learned some lessons about disaster survival in the wake of 2008's devastating Category 2 Hurricane Ike. The Carnival statement said the ship would depart Saturday for Texas to be in position when the Port of Galveston reopens.
Guests whose trips were cut short will receive a prorated refund or can cancel their cruise without penalty, the company said. "Gratuities will also be adjusted to reflect the shortened duration".
Hurricane Harvey has many vacationers anxious about how the storm will impact their plans, especially people planning to take cruises out of Galveston.
As of Friday afternoon, Royal Caribbean had yet to make a decision on how Hurricane Harvey would impact the Liberty Of The Seas. According to the local ABC affiliate, several historical sites in the Galveston area - including the Tall Ship Elissa - have closed and plan to remain shuttered until at least Sunday. To stay up to date, please sign up for text alerts by texting the codes below to CRUISE (278473).
Royal Caribbean is also actively monitoring the path and progression of Hurricane Harvey.