The 25-year-old, who still had another year to run on his current deal, will now be with the O's for another two seasons.
The Frenchman joined from Bournemouth last summer and made 35 appearances in his first campaign under Russell Slade.
Baudry told the club's official website: "I like my life here; I'm enjoying my football, I'm enjoying playing with the lads and I'm excited about the coming season with the team we've got.
"The gaffer has been great too, we spoke towards the end of last season and he knew I wanted to stay so I never even looked elsewhere. I want to stay and confirm what I did last season."
Slade added: "It's fantastic news that we've been able to extend it. Mathieu played a very important part in the second half of last season."