Striker Symes, 28, has agreed a two-year deal with the O's, bringing an end to a two-year spell with the Cherries. The former Everton and Bradford forward netted 11 goals in 37 appearances for Paul Groves' side.
Orient boss Russell Slade told the club's official website: "Michael is a clever frontman with good technical ability and he is a natural finisher.
"I think he can achieve more than he has done in his career to date with the ability he's got, and I'm sure he can show that for us here."
French defender Baudry, 24, has also penned a two-year deal after an 18-month spell with Bournemouth.
Slade added: "I had a long chat with Lee Bradbury, who brought him to Bournemouth, and I feel he can push on and improve further with us. He's a good age, is an aggressive defender and is good on the ball too, so we're looking forward to working with him."
