The 22-year-old becomes Nigel Adkins' third signing of the January transfer window following the arrivals of Donal McDermott and Brendan Moloney.
Raynes, who began his career as a trainee with Stockport, made over 150 appearances for the Hatters.
His departure followed County's acquisition of former Leeds defender Paul Huntington after his contract was cancelled by mutual consent.
Source: Team Talk
