Matthews will join Celtic on a four-year deal in July after his contract at Championship side Cardiff expires.
A club statement read: “Celtic are delighted to announce that they have signed defender Adam Matthews on a pre-contract agreement.
“The 19-year-old, who currently plays for Cardiff City, is one of the most exciting young prospects in the Championship, and it is a real coup for the club to have secured his signing.
“Matthews, a Wales Under 21 international, will join the Hoops on 1st July on a four-year contract, and will link up with his former Cardiff City team-mate and fellow Welshman, Joe Ledley, who has proved to be a great signing for the club already this season.”
