The former Norwich City striker had been without a club since leaving the Canaries at the end of last season.
The 26-year-old told the club's website: "I am happy to be joining Eintracht Braunschweig and I am clearly looking forward to testing myself in Bundesliga 1."
The team's general manager, Marc Arnold, added: "We are happy to have signed Simeon Jackson. He is the second new signing for our attacking lines, he is a flexible player and good on the counter."
Jackson made 19 appearances for Norwich last season.