The departure of the 65,000-tonne warship from Portsmouth Naval Base, Hampshire, was delayed from Friday, August 26, because of a technical issue.
But the £3 billion carrier was able to sail on Saturday afternoon and passed thousands of music-lovers at the Victorious music festival on Southsea Common in Portsmouth.
Pop favourites Sugababes were in the middle of their set when the giant ship sailed past with the crew lining the flight deck to get a view of the festival.
Dancer Sally Turner, of Hoop Shaker which is performing alongside acts on the Beats and Swing stage, waved off the carrier with a display of her hoop skills from next to Southsea Castle in the festival site.
The Nato flagship is sailing to undertake training exercises with the US Navy as well as the Royal Canadian Navy, United States Marine Corps.
The programme is expected to include exercises with the F-35B Lightning jets.
A Royal Navy spokesman declined to comment on the reason for the postponed departure but said: “HMS Prince of Wales’ departure has been delayed. This will not affect her onward programme.”
The spokesman added: “HMS Prince of Wales will cross the Atlantic with her task group, ready to push the boundaries of un-crewed technology and the tactics used by the UK’s two new Queen Elizabeth-class carriers.
“Along with notable port stops in New York, Halifax in Canada, and the Caribbean, the next three months will see the Prince of Wales task group work closely with US allies, operating F-35B jets and un-crewed systems which will define Royal Navy aviation of the future.
“With fleet flagship HMS Queen Elizabeth also set to deploy to the Mediterranean and Baltic this autumn at the heart of a potent Royal Navy task group, it will mean both UK aircraft carriers will be operating F-35B jets thousands of miles apart.”
Commanding officer Captain Richard Hewitt said: “Taking the HMS Prince of Wales task group across the Atlantic for the rest of this year will not only push the boundaries of UK carrier operations, but will reinforce our close working relationship with our closest Ally.
“From operating the F35 Lightnings and drones to hosting the Atlantic Future Forum, none of this would be possible without the efforts of the amazing sailors on board, many of which are on their first deployment with the Royal Navy.”