Shaw, who missed out on selection for the World Cup despite having been part of the initial training squad, had been training with RaboDirect PRO12 side Scarlets during the summer.
However the 28-year-old, who was at Bristol last season, has now agreed a deal with Leeds.
Shaw said: "I am really pleased to be joining Leeds Carnegie. Having met with Diccon Edwards and seen first-hand the style that Leeds want to play this year, it is exciting to be coming into the squad.
"The Championship is a very tough competition but Leeds have got a squad that is looking to compete at the top of the division.
"I will start training this week but I will have to prove my worth to the squad."
Shaw will compete with Dan White and Craig Hampson for the No.9 jersey, with head coach Edwards pleased with the competition in his squad.
"We are delighted to have signed Robbie," he said.
"He was one of the stand out players for Bristol last year and he will give us strength-in-depth in the scrum-half position."
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