Keinhorst, whose Rhinos contract expired at the end of the season, made his decision during the summer before Kevin Sinfield’s return to Leeds as director of rugby.
The 28-year-old never fully established himself in the team under previous coach Brian McDermott and was loaned to Widnes Vikings for a spell earlier this year.
“A decision was made at a different time with different people here,” he said.
“I just felt for my own career to progress I needed an opportunity elsewhere perhaps.
“I spoke with [Rovers’ management] Tim Sheens and then Jamie Peacock and they made it very inviting for me to go there.
“I am looking forward to working with the likes of them and James Webster who I’ve had previously [on loan] at Wakefield as well.
“They haven’t ended too well this season, but hopefully they can have a more positive start to next year and go from there.”
Keinhorst scored 32 tries in 89 games for Rhinos, including one in his farewell game against Toronto Wolfpack last Friday.
The German international made his Rhinos debut in 2012 and his fourth senior game was at Wembley in a Challenge Cup final defeat by Warrington Wolves.
“I am hugely grateful for the opportunity I was given a few years ago,” he said.
“I have made some great memories here and played with some great players and in some great stadiums.
“I am really grateful for the time I’ve had here and everything that’s happened. I’ve made some great friends and that’s what it’s all about.”
Keinhorst identified the 2015 Grand Final win over Wigan – which clinched the treble – as his Leeds career highlight.
“Missing out on the Challenge Cup final that year, just, then coming back and playing a part in the Grand Final, it was special the way that season finished,” he said.
The 17-16 loss to Toronto left Rhinos second in the Betfred Qualifiers, equivalent to 10th in Super League, avoiding the Million Pound Game on points difference.
Keinhorst admitted it was a “disappointing” way to end his Leeds career.
He said: “I wanted to go out with a win and a decent performance, but I don’t think we did ourselves justice.
“I don’t think we’ve performed consistently through games this season and that has cost us in the end.
“We are safe, but it was a disappointing note to end on. I’m quite gutted, but it is what it is.
“Credit to Toronto, they came here and beat us in our own backyard so well done to them.”