Swansea complete signing of Grimes
Grimes has penned a four-and-a-half-year contract at the Liberty Stadium and will be available for the Premier League match against West Ham on January 10.
The England Under-20 international had been the subject of intense transfer speculation after a string of impressive performances for League Two outfit Exeter.
He only made his professional debut in August 2013 and has featured 25 times in all competitions this season.
Grimes arrives at a time when Swansea boss Garry Monk is short on option in the centre of midfield, with Jonjo Shelvey facing a four-match suspension and Ki Sung-yeung heading for the Asian Cup with South Korea.
Exeter, who sit ninth in the fourth tier, revealed that the "substantial fee" made Grimes "comfortably the record sale in Exeter City's history".