The award, chosen by the club's management team, was given to the 23-year-old as the stand-out player over the five matches in the month of September, with the young Borderer showing extraordinary strength and guile as a line-breaking, try-scoring winger.
Jones first signed for Edinburgh Rugby last year after some exceptional performances for the Scotland 7s team and for former club Selkirk.
Less than a season after signing straight from Scotland's domestic divisions, the Borderer was putting pen to paper on a two-year contract extension which keeps him at Murrayfield until at least 2013.
Edinburgh Rugby head coach, Michael Bradley, paid tribute to the youngster's efforts so far this season.
He said: "Lee [Jones] was given the opportunity to perform and has done very well. His performances lifted the team on a number of occasions.
"Some of the highlights would be his defensive work, particularly a covering tackle against Connacht as well as superb line breaks in the match, against Aironi and in our home win over Munster (29-14).
"We've been watching RBS Premier 1 matches since the start of the season and have involved some of these players in games and training. The relationship between seeing players exposed to quality club rugby and us being able to make judgements on their ability is very important going forward, as is evident by Lee's success this season."
Speaking on his award, Lee Jones, said: "It was a bit of surprise to be honest but I'm really pleased to be recognised with the player of the month award.
"I've really enjoyed the start of this season with the highlights being our home win over Munster (29-14) and, as an individual, my try against Scarlets - receiving a ball from a clearance kick presents a good opportunity for a winger so I was really pleased to finish that one.
"As a winger you generally don't get as much ball as the other backs so when you do there's an expectation that you need to make something happen, to break the line or to do something special because the team have put you in that position to finish the move.
"This year I feel a lot more comfortable with that expectation, with making those pressured decisions on the pitch and have settled into life as a professional player.
"I spent least year learning the ropes and getting used to training every day. This year I'm more used to the daily demands, the players around me and the match intensity, so hopefully I can bring more consistency to the team and help us add to our home successes, starting this Friday against Leinster."
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