Richardson was on the look-out for a new club after being released by Southampton earlier in the summer following three years at St Mary's.
He made 68 appearances during his time with the Saints, but featured only five times in the Premier League last season and only once after Mauricio Pochettino's appointment as manager.
Capable of playing across the defensive line, the 30-year-old will provide cover for Boro and becomes boss Tony Mowbray's third summer signing.
Mowbray has previously brought in Dean Whitehead and Jozsef Varga, and is also in talks to sign Bristol City winger Albert Adomah.
Richardson is reported to have agreed a one-year contract at The Riverside, but is not available for Saturday's Championship opener at home to Leicester City.
Meanwhile, Boro have also handed professional contracts to Norwegian defender Birger Solberg Meling and locally-born midfielder Bradley Halliday after the pair caught the eye on trial.