SAN FRANCISCO — Google’s mystery barge floated Thursday to its new home in the California delta after the Internet company was ordered to move it from San Francisco.

The odd-looking, four-story vessel made of recycled shipping containers departed from Treasure Island to comply with a Jan. 31 regulatory order concluding that Google Inc. didn’t have the proper permits to build it there.

Construction stopped on the project late last year.

The barge is similar to one undergoing work on the other side of the country in Portland. That barge, which was assembled in New London, Conn., was hauled by tugboat into Portland Harbor on Oct. 10. It is moored at the Rickers Wharf Marine Facility, where Cianbro Corp. is scheduled to do a significant amount of interior work.

The Portland barge is not under scrutiny by officials because the Rickers Wharf facility is in a land-use zone that allows for marine construction, according to officials with Portland’s Planning and Urban Development Department.

Google says the California barge will serve as an interactive technology center when it’s done. However, various theories have been floated about its purpose. Among the most popular have been that Google is building a party boat, roaming data center or aquatic store.

The vessel’s new home will be Stockton, a city about 80 miles east of San Francisco on the Sacramento-San Joaquin River delta. The Port of Stockton falls outside the jurisdiction of the San Francisco Bay Conservation and Development Commission, the agency that forced the barge to leave Treasure Island.

“It was an exciting morning for us,” said Port of Stockton Director Richard Aschieris. “This doesn’t happen every day. In fact, I would probably say this is, from a maritime point of view, the highest-visibility vessel we may have ever hosted.”

Unlike San Francisco, Stockton has never been a major tourist attraction. The city of roughly 300,000 people fell on such tough times that it filed for bankruptcy in 2012 and is still trying to reorganize its finances under court supervision.

Google has signed a six-month lease to moor the barge in Stockton, Aschieris said.

The attention and intrigue surrounding the barge since it was first spotted last fall have been a source of amusement for Google, which issued a playful statement about its new berth.

“It’s been a busy six months for our barge and it’s grown tired of all the attention, so we are moving it to Stockton where it can have a break, enjoy the city’s delicious asparagus, warmer climate and get a bit of rest before its next chapter,” Google said.