The 49-year-old is rewarded for a successful season that has Orient sitting top of the table on 57 points after 29 matches.
The O's were sat in twentieth position when Edinburgh was appointed last November, following a run of 15 matches without a win, but an excellent second half saw the side finish in a comfortable thirteenth position.
Edinburgh's side have enjoyed a record breaking 2018/19 as they set the club record for longest unbeaten start to a season while also setting the longest ever unbeaten away run.
Edinburgh told www.leytonorient.com: "It was an easy decision for me to sign this extension, there was no second thought, it was just when can we get it done and how long can it be for. I don't think I have been happier for many a year now."
Chairman Nigel Travis added: "Justin has demonstrated in the last 13 months what a great leader he is for Leyton Orient Football Club. We are absolutely delighted that he has agreed to extend his stay with us and I believe this will have a very positive impact on the club as a whole”.