Saint-Maximin is set to complete a £30m to the Gulf State.
Maximin spent four years at Saint James' Park after joining from OGC Nice in the summer of 2019.
He made 124 appearances in total for the Magpies and scored 13 goals.
Saint-Maximin played his part as Newcastle finished fourth in the Premier League last season to qualify for the UEFA Champions League.
Having flirted with relegation in his early years at the club, Saint-Maximin is leaving on a high.
The 26-year-old Frenchman has said his goodbyes in an emotional post on social media.
'4 years ago, I wore the Newcastle jersey for the first time. At that moment, I hadn’t realized that not only was I about to become a Newcastle player, but I was also about to become a Geordie,' Maxim wrote on Twitter.
'Believe me, I fell for Newcastle, I had great opportunities to leave during dark days, but that was too late I was already in love, I wanted, I needed, I had to stay for helping my team to save the club from Premier League relegation because it meant the world for me.
'Of course during those dark days some may have had their doubts, but I always believed in this club and look where we are today, it's just so beautiful.
'I'm leaving Newcastle as it should always have been and that's my greatest trophy because I was a part of it. A deep thank you to ALL of you, my team-mates, the loyal fans, the staff, the Club, etc…
'I’ve seen all your messages, thank you and even though this chapter has ended, the story never stops.
'Newcastle is home now, I'll continue to be your biggest supporter, I'll watch every game and as long as the club keeps winning I'll be the happiest man in the world… and for sure you will see me again.
'I love you, I love you sincerely, I love you like a Geordie brother. Once a Geordie, always a Geordie.'
Saint-Maximin is joining former Premier League players Edouard Mendy, Roberto Firmino and Riyad Mahrez in the Al Ahli squad.
