The 30-year-old has signed a three-year contract, while Rovers have paid a fee of £60,000 to secure the player’s services.
“Whilst I’m sad to leave Hull KR – they have been great to me and my family – I am really excited to be joining Saints,” Burns said.
“It will be great linking with my friend and former teammate Luke Walsh and what is an exciting and strong squad.
“Saints have a strong team that is looking to win silverware over the next few years and I am excited and looking forward to being part of that.”
Burns has made 49 appearances for the Robins, for whom he signed in 2013.
“I want to thank the club first, particularly Neil and Mike Smith, for the opportunity to come to Hull KR,” the player added.
“I was staring down the barrel of a long suspension in the NRL and they gave me the chance to come to a great club and made me and my family feel so welcome whilst we’ve been here.
“Phil Lowe also made a big contribution in getting me to the club so my thanks go to him, as well as to all the coaching staff who made my time with Rovers so enjoyable.
“I’d also like to thank all the players I’ve had the pleasure to play with because I’ve made some great mates at Hull KR and I’m leaving a better player than when I arrived.
“Special thanks too to all the fans. They’re the most loyal and passionate fans that I’ve come across in my rugby league career and I’ll really miss running out in front of the East Stand.
“Leaving the club will be sad but it’s a decision I had to make in the best interests of my family. We only get a small space of time in rugby league to do the best we can and the opportunity at Saints was in the best interests of both parties.
“I’ve always played with pride and passion whenever I’ve pulled on the Rovers jersey. I always gave 100 per cent and I’d like to think that I’ll be welcomed back by the fans.
“I’ll always be rooting for Hull KR and I know the club has a good future with the people on board for next season.”
St Helens coach Nathan Brown is delighted to have added to his halfback options for next season.
“Travis is a great competitor and will bring that to the club,” he said.
“He will also add good depth to our halves and we’re looking forward to having him on board.”