The 23-year-old Germany international centre will now remain with the club until the end of the 2016 Super League season at least.
"I am pleased to have agreed the new contract and I am looking forward to a big pre-season and trying to earn my place in the squad for 2014," he told the club's official website.
"The experience of training and playing with world-class players at Leeds has helped me develop my game and hopefully I can continue that process next season and beyond."
Rhinos head coach Brian McDermott said that Keinhorst has shown "great maturity" over the past few months and is looking forward to working with him over the next three years.
"We are delighted that Jimmy has agreed the new deal and I look forward to seeing him develop even further over the next three years," he said. "Securing Jimmy adds to the strength in our squad and that will be important next season.
"He showed great maturity last season to continue to work hard on his game whilst at Hunslet Hawks and earned a recall to the first team through his own commitment and attitude which bodes well for his future development."
Keinhorst has been capped eight times by Germany.