Defender Clohessey, 28, arrives on a free transfer from Colchester and 27-year-old midfielder Moore joins after bringing an end to a five-year spell with AFC Wimbledon at the end of last season.
New Orient boss Ian Hendon told the club website: “Both Sean and Sammy are very good signings for us.
“They have plenty of experience at this level and I believe they can both slot in with the minimum of fuss and for me, that’s great.
“It’s been non-stop for me since I was appointed and it is nice to be able to confirm our first two new additions to the squad.
“Sean is a great crosser of the ball and will add a lot to our play going forward, while also being a good defender. For me when he became available it was no-brainer.
“Sammy has been a great player for AFC Wimbledon over the years and he will give the team plenty of energy. He doesn’t stop running and again he has the experience of this level to do well for us.”