Jones previously worked at Neath, the Ospreys, where he saw them to two Magners/Celtic League titles and the EDF Cup, and the Dragons.
The former Wales international will now move to the ambitious Championship club from his position of director of rugby at The British School Al Khubairat (UAE) in Abu Dhabi.
Jones will now look to build on London Welsh's success over the past two seasons, with the Exiles having reached back-to-back play-off semi-finals.
Jones said: "I am extremely pleased and honoured to be offered an opportunity to coach a club such as London Welsh. It is steeped in tradition and history, with a desire to return to the top of the English game.
"I will bring my experience and understanding of coaching at the top level to a side that has ambition. Closing the gap between Aviva and Championship rugby takes a lot of hard work to create more consistent individual performances.
"To be successful in this environment is not just about your own ability and work ethic, it's about surrounding yourself with people of ability and experience of what it takes to succeed in the professional game."
Jones replaces Greening, who left the club by mutual consent at the end of the season, with the club impressed with his vision.
"We are very excited about this appointment," said London Welsh managing director John Taylor.
"Lyn has already proved himself at the highest level and has really bought into our vision of the way forward for this great club. He has a rare coaching talent and the fact that he is Welsh is an added bonus."
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