The 20-year-old winger has been given permission to undergo his medical, according to The Athletic. Transfer expert Fabrizio Romano has also reported that the deal is done, with the fee worth a total of €50m.
Touré is expected to sign a multi-year contract with Newcastle shortly.
The Ivory Coast international left Swedish top-flight side Hammarby IF for Hoffenheim in January 2025.
That move was worth SEK 140m, plus a further SEK 20m in bonuses, with Hammarby also inserting a sell-on clause into the deal. Since arriving at Hoffenheim, Touré has scored five goals and provided 15 assists in 45 competitive matches.
He had long been chased by bigger clubs, primarily from the Premier League, before Newcastle won the race for his signature. The sell-on clause means Hammarby stand to collect further millions from Touré's departure.
Hammarby's sporting director, Mikael Hjelmberg, confirmed the existence of the sell-on clause.
"If the transfer goes through it means a welcome addition to an already stable budget without any great effort on our part," he told Expressen.
The transfer represents a significant windfall for the Allsvenskan club, who first sold Touré for SEK 140m plus bonuses just eighteen months ago.
Newcastle United's pursuit of Touré comes as the club continues to strengthen its options across the forward line this summer.