The 20-year-old midfielder will remain at the DW Stadium for the remainder of the season after failing to make a first-team appearance for Chelsea since Jose Mourinho returned as manager.
McEachran spent 2012-13 on loan at Middlesbrough and played the first half of the current campaign at Watford, where he made seven Championship appearances.
"This is a big scoop or us," Rosler told the club's official website.
"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.
"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."
