The 31-year old left-back, who can also operate as a winger, will become a Quakes player pending the receipt of his P-1 visa and International Transfer Certificate.
"We're very excited to add Jordan to our squad," said Watson. "He came and trained with us last year and did very well.
"He brings a lot of experience at the highest level of soccer and he will be an excellent addition the club."
: San Jose general manager John Doyle added: "Jordan adds depth to our squad as an attack-minded left midfielder and left defender. We look forward to him joining the club."
Stewart started his career with Leicester in 1999, before moving to Watford in 2005, following a loan spell with Bristol City. He then signed with Derby County in 2008, moved onto Sheffield United the following year, and even tried his luck in Greece with Skoda Xanthi.