The Iranian international was signed from AZ Alkmaar in 2018 and made 61 appearances.
Head coach Graham Potter said, “Ali has been a very good professional and great to work with, but this move is a good one and gives him the chance of more regular game time, which is not something we are able to guarantee.
“I’d like to thank Ali for his hard work during my time here and wish him all the best for the future.”
Jahanbakhsh scored four goals for Albion, the most memorable his overhead kick against Chelsea at the Amex on New Year’s Day 2020.
That came a few days after his first goal for the club, another standout strike in a 2-0 win over Bournemouth.
Alireza began his career with the Damash Gilan youth academy in Iran, before moving to Iranian second division side Damash Tehran in 2010.
He returned to Gilan a year later and became one of the club’s youngest ever players, making his senior debut in 2011 at the age of 17.
He then moved to Holland and signed for NEC Nijmegen in 2013, for whom he made 64 appearances and scored 19 goals, winning the Dutch Eerste Divisie title in his second and final season at the club.
A move to Alkmaar followed in 2015 and the Iranian was the top scorer in Eredivisie in 2017-18, where he netted 21 goals in 33 appearances.
He also has earned more than 40 caps for Iran and featured in all three of their games at the 2018 FIFA World Cup in Russia.