The 24-year-old joins the Seagulls from Dutch side AZ Alkmaar, where he finished last season as the leading scorer in the Eredivisie with 21 goals in 33 appearances.
Jahanbakhsh, who was part of Iran's squad at this summer's World Cup, has put pen to paper on a five-year deal at the Amex Stadium, joining in a move thought to be worth around £17m.
"We are delighted to welcome Alireza to the club, and we are particularly pleased to get this deal over the line," manager Chris Hughton told the club's official website.
"Ali is a player that we have been aware of and monitored for a few years, and his versatility will increase our attacking options within the squad.
"He can play in a wide position or central midfield attacking role, and I am now very much looking forward to working with him."
Jahanbakhsh becomes Brighton's eighth major signing of the summer.