The 27-year-old has been unable to convince coach Joe Schmidt that he deserves to be first-choice in a fully-fit squad over the past 18 months.
"I'm delighted to have re-signed for Connacht. I thoroughly enjoyed my three seasons there and I can't wait to get back to the club and continue to improve my game," said Carr.
"I can see that there is fantastic work being done at Connacht both on and off the field. I'm really looking forward to being part of that again and contributing to the growing success over the next couple of seasons."
Meanwhile, Munster's Peter Stringer has joined Premiership club Bath on a short-term contract.
"Munster have reached agreement with Bath Rugby for Peter Stringer to join the English Premiership club on a short-term contract," said a Munster statement. "Stringer will join Bath this week and remain there on a 7/8 week loan basis. He will be available to Munster for the Heineken Cup knock-out stages if required."