The Australian full-back, 31, has proved a stellar performer for Saints since joining from North Queensland Cowboys, helping them win the 2019 Grand Final in his debut season and retain the title last year.
Coote also won the NRL Grand Final with Cowboys in 2015, alongside Kane Linnett, his Scotland team-mate who he will link up with once more at the Robins next term.
A Great Britain tourist in 2019, when he also made the Super League Dream Team, he is the latest in KR's high-profile signings after they brought back England winger Ryan Hall from Sydney Roosters this year.
Coote says Rovers coach Tony Smith was influential in him turning down the chance to stay with champions Saints and move to East Yorkshire.
“That was the main reason to sign for the club really," he said.
"I was having some great chats with Tony on what Hull KR are all about, and what they have in place really appealed to me.
“I’m really big on having that player-coach relationship. Tony was big on it as well, making sure that we could work with each other.
"I’m really excited for the challenge too, a new start and a move to the other side of the country."
Rovers, who finished bottom last term, are up to fifth having won four of their last five games.
“To move on to Hull KR is exciting," added the ex-Penrith Panthers player.
I think the club itself is heading in the right direction. I’m really excited to get across there and see what the City and the fans are all about.
“I know you guys have got a good backing with the fans, so I’m really excited to get out in front of them.”
Smith added: “He’s a good lad. He has plenty of experience and he is ready for a change, and I think we’ll be a good fit for him.
“As we have seen with form since he arrived in the UK, he’s proven to be one of the most consistent performers in Super League.
“He is still a top-class Super League player, and he brings a professional mentality.
"Winners have a good professional attitude to their job. He’s been really keen to join us and add to what has already been a very successful career.
“Some of the ways that made a player like Lachlan consider us is the way that we are performing on the field. It’s made some people stand up and watch us in different ways.
“We’ve changed the calibre of targets that we have been after, and we have been fortunate to get someone of Lachlan’s quality to join a group of people that are working really hard at the moment to be more and more successful.”