The 16-year-old ended a nine-year association with Liverpool over the summer after turning down scholarship terms at Anfield, joining Arsenal instead following talks over compensation between the two clubs.
Joseph, the younger brother of Valentin Joseph — who moved from Blackburn Rovers to Brighton earlier this year — is eligible to represent Nigeria, England or Germany at international level, but has so far represented the Three Lions at youth level.
His goalscoring record explains the level of interest he generated. Joseph scored three goals in his first two under-18 appearances for Liverpool last season, and has been even more prolific for England's under-16s, netting eight times in nine appearances and adding an assist.
Arsenal will be hoping that record translates into an immediate impact at academy level as they push for honours this season.
At Arsenal, Joseph reunites with players he already knows well from international duty, including Emerson Nwaneri and Charlie Phillips, with his partnership alongside Nwaneri having already proved productive for England's youth sides. The club will hope that understanding can be replicated in Arsenal colours.
Joseph's arrival continues an active summer of academy recruitment in north London, with Arsenal also bringing in Andria Bartishvili, Phoenix Blayney, Habeeb Ogunneye, James Scanlon, Igor Tyjon, Axel Donczew, Mylo Bernard and Elijah Upson across various age groups, as the club continues to invest heavily in strengthening its academy pipeline.
The move represents a blow for Liverpool, whose academy has built a strong reputation in recent years for identifying elite young talent early, having previously developed the likes of Harvey Elliott, Ben Doak and Trey Nyoni before they broke into senior football.
Losing a prospect of Joseph's profile to a direct Premier League rival will sting, even as Liverpool continue to invest heavily in their own pathway.
For Arsenal, the deal is the latest sign of their growing willingness to compete directly with domestic rivals for the country's most promising young talent, rather than relying solely on their own academy structure to produce it.