The 49ers announced the deal Friday.
The 6-foot-1, 250-pound Bellore has spent his first four years with the New York Jets. He has three tackles and 90 special teams tackles in his career.
Last season, Bellore ranked second on the Jets with 15 special teams tackles. He led the team in special teams tackles in each of his first three seasons, including a career-best 31 special teams tackles in 2011.
The 25-year-old native of Whitefish Bay, Wisconsin, played at Central Michigan before signing with the Jets as an undrafted free agent in 2011.