It will be the first time that the team has fielded two riders since they made their debut in the sport in 2006.
The 19-year-old, who currently leads the Moto 3 world championship, said: "I'm very happy to make the leap up to MotoGP next year, especially because I will do so alongside HRC. It's a dream come true.
"I think that every rider would like to race at the highest level in the World Championship with a Honda. It is certainly a big jump from Moto3 to MotoGP, but I am convinced that we are ready and that, step-by-step, learning every day, we can do a great job.
"In the meantime, I remain fully focused on this season's Moto 3 World Championship. I will have to avoid any distraction in order to fight for the title."
Crutchlow announced that he would be moving to the team following a disappointing season with Ducati last month.