The 24-year-old, who played 16 games on loan at Kilmarnock last season, will compete with James Tavernier.
Hodson started his career at Watford and played 51 games in three seasons at MK Dons after a loan at Brentford.
He joins new faces Matt Gilks, Clint Hill, Joey Barton, Niko Kranjcar, Jordan Rossiter, Matt Crooks and Josh Windass at Ibrox.
Rangers paid an undisclosed fee for Hodson, who was part of Northern Ireland's squad at Euro 2016, but did not feature in any of their four matches.
Rangers have made right-back Lee Hodson their eighth summer signing on a three-year deal from MK Dons.