A counter at thepiratebay.se showed a countdown to 1 February, but it appears to have come back online a day early.
The website, which provides links to pirated content, was taken offline following a raid in Sweden in December.
Police officers seized servers in Stockholm after a complaint was filed by a group called the Rights Alliance, which targets internet crime.
The police operation took place in an area in Nacka, south-east of Stockholm, with the area's cold weather used as a natural cooling system for computer servers.
The site was taken down in 2006 after another raid by police but reappeared online three days later.
The Pirate Bay is one of the internet's most-visited websites, and the film, music and software industries blame it for losses running into billions of pounds.
Internet service providers (ISPs) in the UK were ordered by the High Court to block access to the site in 2012.
In October Pirate Bay co-founder Gottfrid Warg was sentenced to three-and-a-half years in prison for hacking into computers and illegally downloading files.
Another co-founder, 35-year-old Peter Sunde, was arrested in Sweden last year after two years on the run and was sentenced to eight months in prison for violating copyright laws.
Meanwhile a third co-founder, Hans Fredrik Lennart Neij (known to hackers as TiAMO), was arrested while trying to cross into Thailand from Laos in November.
A message from "Winston" on the newly-relaunched site reads: "So, first we ditched the trackers. We even got rid of the torrents. Then we left the servers to enter the clouds.
"Now, we're about to take the biggest step in our history."
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The Pirate Bay website has been relaunched.