Oxlade-Chamberlain, 32, has penned a contract at Celtic until the end of the season with the option to extend his stay in Scotland for another year.
The Saints academy graduate has been without a club since leaving Besiktas in August and has not played since May.
“Speaking with the manager, it just felt like the perfect fit for me, and I feel like I can come in and help out the lads,” said Oxlade-Chamberlain.
“Just talking to the manager, he told me the expectations on the club and what it means to play here, what our targets are, and that he’s going to push me.
“That’s all the stuff I identify with, and that’s the environment I’ve always been in and been lucky enough to be in. It’s exactly what I need.”
Oxlade-Chamberlain played 43 times for Saints, scoring 10 times and notching nine assists, before making a big-money move to Arsenal in 2011.
He had been training with Arsenal before making the move to Celtic, who currently sit third in the Scottish Premiership.