The 35-year-old played a key role in Orient`s charge away from the League One relegation zone last season, scoring six goals to help the O`s to a 14th place finish.
McGleish, who was released on a free transfer by Wycombe, becomes the third O`s player to agree new deals with the club following Loick Pires and Andrew Cave-Brown.
Boss Geraint Williams is now waiting to hear from midfielder Sean Thornton, who has yet to sign a new contract.
Thornton had been linked with a summer switch to Shrewsbury after enjoying a successful loan spell with the Paul Simpson`s men earlier in the season.
But Shrewsbury`s defeat to Gillingham in the League Two play-off final may have ended Thornton`s hopes of moving back to the New Meadow.
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Scott McGleish is a good player and worth keeping
McGleish will scrap it out but he’s getting old. Where are the young players who can get those goals in the future?
He could be a good foil for Patulea who if he doesnt score a hatfull of goals Ill eat my hat.