The left tackle, who had been placed under the team's franchise tag earlier this year, is set to earn up to $57.5m (£38.2m) through the deal, with $33m (£21.9m) guaranteed.
The 26-year-old told ESPN: "It was pretty hard to pass up $33m guaranteed. That is pretty solid. The structure is a lot better from last summer."
Clady, who started all 16 games for the Broncos last season, is continuing his recovery from shoulder surgery earlier this year.