The Frenchman signed for the O's from Bournemouth at the end of last season and went on to make 35 appearances for the club in 2012/13.
Baudry had one year left on his contract, but has now pledged his immediate future to the east London club.
He told the club's official website: "I'm very happy for it to be done, it's been agreed in principle for some time, but there were a couple of minor details to sort and I'm glad it's done now.
"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.
"The fans have always had in confidence in me and that really helps and I want to stay and do well for them."