Quaresma, 30, played for Porto between 2004 and 2008 and was a free agent having most recently been with Al Ahli in Dubai.
"I am happy to return to a home I know well, where I can feel the love and faith of the fans," said the player in a statement on the club's website.
More than 10,000 supporters attended an open training session on New Year's Day in which Quaresma took part.
The player has also played for Sporting Lisbon, Barcelona, Inter Milan, Chelsea and Besiktas.
Defending Portuguese champions Porto currently sit second in their domestic league, level on points with leaders Sporting and third-placed Benfica.
They were knocked out of the Champions League at the group stage but will play in the knockout phase of the Europa League, a competition they won in 2011.
Portuguese winger Ricardo Quaresma returns to Porto
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