Rev Thompson, who has served in the Diocese of Manchester for 23 years,will be installed during a ceremony at the West Midlands landmark in September.
He said: "I am very honoured and delighted to be the next Dean of Birmingham and to serve the Cathedral and the communities of the Birmingham diocese.
"I am looking forward to leading a wonderful team at the Cathedral and to joining the Cathedral community. I am very drawn by the desire of everyone at Philip's to reach out to the parish, city and diocese they seek to serve.
"I am very fortunate to be following the footsteps of my predecessor Dean Catherine Ogle and I hope to build on her excellent work in building partnerships across the city and the diocese."
Big news! We will be welcoming Matt Thompson as our new Dean in September. Read more https://t.co/AZW98AjT6b #newbeginnings #cathedrallife pic.twitter.com/QOAZPk4tDG
— Birmingham Cathedral (@bhamcathedral) May 7, 2017
The arrival of Rev Thompson, who is married and has a ten year old daughter, will follow the departure of Very Rev Catherine Ogle earlier this year.
Bishop of Birmingham, Rt Rev David Urquhart said: "I am delighted that Matt has been appointed Dean of Birmingham at such an exciting time in the life of both the church and the city.
"Matt brings with him a wealth of experience and a passion for the Gospel. We are really looking forward to welcoming him and his family to the city and region, and to working together in the service of Jesus Christ."
Rev Thompson has been a vicar at Bolton Parish Church since 2008.