The Portugal captain, 37, is a free agent after leaving Manchester United following a controversial interview in which he criticised the club.
Al Nassr, nine-time Saudi Pro League champions, described the signing as "history in the making".
BBC reports the club said it would "inspire our league, nation and future generations to be the best version of themselves".
Earlier this year, Ronaldo turned down a $580m deal to join another Saudi team - Al Hilal - because he was happy at United.
