The Swedish right-back joined Newcastle United from Amiens SC in the summer of 2019 and leaves having made 106 appearances, winning a Carabao Cup winners' medal along the way.
This season has been defined by injury. Krafth suffered a knee problem while on international duty with Sweden and has not featured for the club since November. Before that setback, he had made just one Premier League appearance all campaign.
Head coach Eddie Howe paid tribute to the 31-year-old on the club's official website.
"Emil has embodied what it means to be a Newcastle United player on and off the pitch. He's been a brilliant servant to the club and he absolutely deserves the send-off that I know he'll get at St. James' Park this weekend."
Krafth will receive a half-time presentation at Sunday's home fixture against West Ham United.
The player himself reflected warmly on his time on Tyneside.
"I'm so grateful to have had the opportunity to represent this incredible football club for the past seven years. It's been a huge part of my life, I've made some amazing memories here and Newcastle is somewhere I've been really proud to call home."
The departure had been widely anticipated. Transfer journalist Nicolò Schira reported in February that an extension was unlikely, and while Krafth did sign a short contract extension earlier this season to keep him at the club through 2025/26, no further deal has been forthcoming.
Sporting director Ross Wilson added his own tribute, with Sunday's game offering what he described as a chance for supporters to show their appreciation for a player who had served the club with consistency across multiple eras.
Krafth's seven years at St. James' Park spanned the final years of the Mike Ashley ownership and the transformation that followed the Saudi-led takeover in 2021. He played a dependable role in the early Howe years that delivered Champions League football to Newcastle for the first time in two decades.