The centre-back joins Die Kraichgauer on a five-year-contract from Swiss outfit Young Boys.
He made 50 and 12 league appearances and European inter-club outings respectively over two seasons with YB.
"The fifth newcomer to TSG Hoffenheim is Kasim Adams Nuhu," the German club announced on Wednesday.
"The 23-year-old defender comes from Swiss Champion Youngs Boys Bern. The Ghanaian international signed a contract with the Bundesliga club until 30 June 2023.
"After Kasim Adams Nuhu successfully completed the compulsory medical check-up in Heidelberg on Tuesday afternoon, the two clubs agreed on the final terms of the transfer in the evening.
"Nuhu was impressed by the conditions at the future Champions League participants and highlighted the discussions with the TSG officials."
Adams will wear the No.15 jersey at his new club.
"I felt welcomed and wanted from the very first moment, so I was a little bit impatient in the final moments [of negotiations]," said, the defender.
"I wanted to finally get started in Germany. Now, it's time and I'm very happy about the challenges of the Bundesliga and Champions League as well as working with this young team here at TSG."
TSG manager Alexander Rosen expressed delight by their new addition, describing the Ghanaian as "strong with great potential to impress immediately with his exceptional physique."
For the club boss, Adams has a "stable play structure and an extreme header strength, which will do us well both defensive and offensively."
Adams joined Young Boys on a permanent deal from Spanish outfit Real Mallorca last year following an initial loan deal.
He played for local side Medeama during his time in Ghana.
The Black Star made his international debut against Saudi Arabia last October, scoring in the 3-0 triumph for Kwesi Appiah's outfit.