The 23-year-old enjoyed a successful spell on loan with Boro in the 2014-15 season, scoring 19 goals in a season where he also won the Championship Player of the Year.
However, in the past couple of seasons, the ex-England U-21 international failed to impress while on loan with Crystal Palace, Norwich and Burnley in the Premier League, failing to score a single goal.
In over four years at Chelsea, he failed to make a single appearance for the Blues, but Chelsea are still set to make a tidy profit of up to £8.5m after signing the striker for £1.5m from Nottingham Forest.
Bamford has signed a four-and-a-half deal with Boro and will hope to help Aitor Karanka's side avoid relegation back to the Championship.