The centre back joins The Reds from Scottish Premiership side Aberdeen, moving to The City Ground for an undisclosed fee.
Scotland international McKenna started out in the youth ranks at Aberdeen, making his professional debut in 2016.
The 23-year-old made over 100 appearances for The Dons, including in the Europa League, and claimed the Player of the Year award in 2017-18, his first full season with the club.
McKenna has made 16 appearances for his country and now moves south of the border to team up with the Nottingham Forest squad.