The 23-year-old German, who won the Moto2 title in 2011, made his MotoGP debut with Lucio Cecchinello's team last year.
Bradl is currently sixth in the championship, having secured his maiden pole position and podium finish at Laguna Seca earlier this month.
Bradl will be a 'factory-supported' rider, meaning he will continue to receive direct support from Honda Racing Corporation.
"HRC's support was extremely important for me in my first season in the premier class and, with their direct co-operation, I achieved my first podium in the top class this year," said Bradl.
"I am happy to continue with Lucio's team because we know each other very well now and we have built a professional and friendly atmosphere in the team that allows me to be at 100 per cent every race".
HRC vice-president Shuhei Nakamoto said: "HRC is happy to continue working with Stefan in the LCR team in 2014.
"He is showing the performance we expected and he is working very well with Lucio's team.
"We believe in them and we look forward to seeing Stefan on the podium again soon and many times in the future."