The 28-year-old, who had been without a club since leaving Oldham at the end of last season, has joined the League One leaders on a free transfer.
Orient manager Russell Slade told the club's official website: "Robbie could prove to be a really handy signing for us.
"We know we have a small squad so need players that are versatile and he can play up front or in midfield plus he's a great character to join the group too.
"We need to find out where he is in terms of his fitness as he's been at a few clubs over the summer but not had a full pre-season but we'll soon get him up to speed."
Simpson has also previously played for Coventry City and Huddersfield Town.