The 19-year-old had been linked with a number of Championship clubs, but has now signed a deal with Boro.
The youngster has joined Boro on a season-long loan.
McEachran made just five appearances while on loan at Swansea last season.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.