The England Under-21 international will spend the 2017-18 campaign on-loan at the Riverside Stadium from Chelsea, although his long-term future remains at Stamford Bridge as he has also put pen to paper on a new five-year contract with Antonio Conte's side.
Baker's immediate priority, however, is to help Boro secure an instant return to the top flight following their relegation last season.
"It's going to be an exciting season," Baker told the club website. "I'm here to give my input and hopefully get the club back to the Premier League."
Boro lost their opening match of the new season, going down 1-0 at Wolverhampton Wanderers last weekend, but they will be hoping to return to winning ways when they play host to Sheffield United on Saturday evening.