Rosler said that McEachran, who spent last season on loan at Middlesbrough, is one of the brightest English talents and that he is looking forward to helping his development.
"This is a big scoop for us. There's no doubt Josh is a huge young talent, and we have worked really hard to convince him and Chelsea this is the right place for him to be for the rest of the season," he said.
"I thank everyone for their efforts in making the move happen. Hopefully, we will be able to help each other, he can bring something to our team and we can help in the development of one of the country's finest young talents."
McEachran has 13 caps for England's Under-21 side.