The 25-year-old Brazilian leaves the Baggies after two successful years, scoring 20 goals in 77 appearances.
Pereira was the star of the club’s promotion to the Premier League under Slaven Bilic in 2019/20 and impressed in the top flight last season as well – grabbing a brace in the 3-2 victory at fierce rivals Wolves.
However, he told Albion he wanted to leave following their relegation back to the Championship and after a public spat with boss Valerien Ismael, his departure has now been confirmed.
Speaking after last weekend’s friendly win over Birmingham, Ismael revealed Pereira was not being considered for selection as we was ‘not committed’ to the club.
The playmaker then hit back to say he felt ‘disrespected’ and had remained professional despite the ‘life-changing’ offer from Al Hilal.
Pereira is expected to earn in excess of £100,000 a week in Saudi Arabia.
He took to Twitter to express his gratitude for his time at The Hawthorns as he said: "Gratitude. This is the feeling that I have for the club that opened the doors for me two years ago. The club that believed in me, in my work, and gave me some of the best moments of my career.
"It was goals, passes, dribbles, defeats, but mostly victories I had with this shirt, and some of them out of field. Those victories came with the support and care that the Baggies' fans always had with me.
"Those victories came with the politeness and great treatment that every employee of the club had with me and my family.
"Given all of this, the feeling couldn’t be other than gratitude.
"Matheus is going to another challenge, but part of him stays here, in blue and white, and always cheering that this shirt always have the success that deserves. Thank you all! C’mon Baggies!"
The Baggies, meanwhile, said as part of a short statement announcing the move: “The club wishes Matheus well in his future career.”