The Aviva Premiership club are in grave danger of going into administration unless they can attract new investment by the end of the campaign, following the collapse of takeover talks.
Wasps chairman Mark Rigby on Tuesday issued an appeal for potential new backers to step forward, promising the club would make "a strong impact next season".
Jones, who has won 104 caps for his country, and Johnson will be joined in the Wasps squad by the returning England internationals Tom Palmer and James Haskell.
Wasps have also signed props Phil Swainston from Leeds and Will Taylor from the Ospreys.
London Wasps chief executive Chris Thomas said: "While everyone is aware that the club is seeking investment as a matter of urgency at the moment, in terms of player recruitment and retention, like every other club at this time, we have been working hard to continue to put our squad together for next season.
"We are very pleased to have recently secured these excellent signings whose quality will place us in a strong position for next year. But, while it is pleasing to announce further additions to the squad, of course our priority now is concluding a deal which will secure our financial future."
Jones, 34, is the sixth leading international points scorer of all time and he has made six Test appearances for the British and Irish Lions.
Johnson began his career as a hooker but a move to the back row earned him three South Africa caps in the 2011 Tri Nations.
Jones said: "I feel this is the right time to move on at this stage in my rugby career - the Scarlets are showing such promise and have plenty to build on for the future with a very talented group of emerging players who are only going to go from strength to strength now.
"I feel very privileged to have been part of this great club for so many years and particularly the new era - with a team that now has so many exciting new players coming through and achieving international honours. I hope I've been able to pass on some of my experience for the benefit of our future as a region and helped accelerate the transition of this squad in recent years.
"It's been a huge part of my life being a Scarlet - starting when I was 18 and now leaving when I'm 34 and apart from a couple of years in France its where I've grown up as a rugby player. I've been delighted to be part of Scarlets Rugby throughout and it has been an honour to pull on the shirt every single time."
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