The 38-year-old, who brought Ipswich back to the Premier League after a 22-year absence, defeated Manchester City’s Pep Guardiola and Arsenal’s Mikel Arteta for the accolade.
The LMA’s shortlist also included Everton manager Sean Dyche, Aston Villa’s Unai Emery, and Portsmouth manager John Mousinho.
Guardiola was already named Premier League manager of the season, while Liverpool’s Matt Beard received the Women’s Super League manager of the season award.
McKenna, who was born in London and bred in Northern Ireland, left Manchester United as first-team coach in December 2021 to take over at Ipswich, which was then in League One.