London Welsh currently sit third in the Greene King IPA Championship table, as the club looks for an immediate return to the Aviva Premiership.
Commenting on signing a new deal with the club, Burnell said: "Before joining London Welsh I'd previously only worked in one professional rugby environment, at Cardiff Blues, where we enjoyed a huge amount of success.
"After leaving, I was given a fantastic opportunity by London Welsh to coach in a professional environment again, and the experience has been a breath of fresh air and one I've thoroughly enjoyed.
"For that I'd like to thank Kelvin [Bryon] and Bleddyn [Phillips] for the trust they've placed in me, but my biggest thank you must to go to Steve Lewis for introducing me to the club. It's down to Steve that I'm at London Welsh.
"The preparation at London Welsh is no different to the preparation at Cardiff Blues going into a Heineken Cup semi-final or Amlin Challenge Cup final. It's been fantastic.
"The reason why we had success at the Blues was because of the culture and work ethic within the environment, and we've put the same principles in place at London Welsh.
"Assistant coaches Gordon Ross and Ollie Smith, the strength and conditioning department led by Ryan Campbell and the medical department led by Chris Jenkins have been crucial to that, and have all played a huge role in getting us to where we are this season.
"London Welsh is a family which includes the junior section, the amateurs and the club's supporters. My son plays for the juniors and I've built up a good relationship with all of the different sections of the club. That was also a factor in my decision."
London Welsh chairman Bleddyn Phillips said: "I am absolutely delighted that Justin has agreed to extend his tenure with London Welsh. He has been a tremendous influence since coming on board last year, instilling a team spirit within the club, the players and supporters alike, and this has been clearly evidenced in the performances on the field this season."