Fletcher joins on-loan with an option to buy at the end of the season.
The 19 year-old spent past of last season on-loan with Swansea City.
Forest's Head of Academy Chris McGuane said: “I am delighted to welcome Kristian to Nottingham Forest and we are very happy to add the quality he has to our B Team squad.
"He brings experience of playing in the MLS and with the potential he has, we are looking forward to working with him and watching him progress further as a player.
"We are excited to see the impact and development that he will make, and it is credit to our excellent recruitment team lead by our Head of PDP and Emerging Talent Recruitment Dan Kelly that we can bring Kristian to Nottingham Forest.
"Everyone at Nottingham Forest wishes Kristian all the very best as he starts what will be an exciting time for him at the club.”
Fletcher added: “I’m happy to be here and buzzing to get started.
"I knew Forest was a big Club, but being at the stadium and understanding more about the history, I now can’t wait to meet my teammates and get going.
"I want to keep learning and developing and I'm confident this is just the start of what will be an incredibly rewarding journey with Forest and our fans."