The 23-year-old Scotland international has agreed a three-year deal with City and will join the club when his contract with Caley runs out in the summer.
Shinnie has scored 15 goals in 41 appearances this season helping Terry Butcher's side to their current position of third in the Scottish Premier League.
The former Rangers player also made his international debut this campaign during a friendly against Luxembourg in November.
He spent most of the 2008/09 season and the second-half of the 2009/10 campaign on loan at Dundee from Rangers before making a permanent switch to Inverness in the summer of 2011.
His goalscoring record for the Highlands club is impressive with 23 goals from 62 appearances.