The 24-year-old has joined the club on a four-year-deal, per a statement from Boro.
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While the club have not disclosed the fee, it is believed to be in the region of £4 million.
Joseph arrives on Teesside after netting eight times and registering five assists in 44 appearances for The Tigers during the 2025/26 campaign.
After signing for Boro, Joseph said: “I’m so delighted to sign for this massive club.
"It’s such an ambitious club and I really want to help it achieve its goals.
“I’m an all-action centre forward, but most importantly I want to score goals and help the team win games.”
Joseph is now expected to meet up with his new teammates at their pre-season training camp in Portugal.