McKenna, 38, led the East Anglian club to a second successive promotion last season as Ipswich returned to the Premier League.
That achievement saw him linked with the managerial vacancies at English top-flight rivals Brighton, Chelsea and Manchester United.
“I am extremely proud to have signed a new contract with the club,” McKenna told Ipswich’s website.
“We have enjoyed incredible success together over the last two seasons and I’m excited to have the opportunity and responsibility of leading this fantastic club into its first season in the Premier League in 22 years.”
The Northern Irishman added: “Preparation and planning for the challenge ahead has been ongoing since we won promotion at the beginning of May, with plenty of work still to do before the start of the new season at what is such an exciting time for everyone at the club.
“I am so happy to have committed my future to taking the next step with Ipswich Town and am really excited for what’s ahead as we continue this journey together.”
The former Manchester United youth coach’s extended deal is set to keep him at Portman Road until 2028.
Assistant manager Martyn Pert, first-team coaches Charlie Turnbull and Lee Grant and head of goalkeeping Rene Gilmartin have also extended their contracts with the club.
“We are delighted Kieran has further committed his future to the club,” said Ipswich chief executive Mark Ashton.
“Success brings its own challenges and there has been considerable speculation in recent weeks, but Kieran and I have continued to communicate throughout, often several times a day, as we plan for the club’s first Premier League season in a generation.”
Ashton added: “For Kieran to have signed a new contract is a significant boost, heading into such an important campaign, as we continue the hard work in preparation for the coming season.”
Ipswich followed their promotion from English football’s third-tier League One by finishing runners-up in the Championship to Leicester.
They lost only six league matches and ended the season with 96 points, having scored a division-best 92 goals.