The 25 year-old midfielder has signed for £1.25m on a three year contract. The fee could increase as it is linked to future appearances and whether West Brom stay in the Premiership.
Greening has had three years at the Riverside. He was signed from Manchester United by Steve McClaren who brought in Mark Wilson (also from Manchester United) at the same time.
After a good season in 2002/03 Jonno failed to capture a regular starting position last season. With the arrival of Ray Parlour and possibly Bolo Zenden his opportunities at Boro next season were not looking good. Hence a move to hopefully play regular first team football and rebuild his career.