The MP has also announced he has resigned from the Conservative Party.
Mr Stewart tweeted: “It’s been a great privilege to serve Penrith and The Border for the last ten years.”
I am running as an Independent candidate for Mayor of London, and here’s why.
He was expelled from the Conservatives in the Commons along with 20 other Brexit rebels, but remained a member of the party.
In the Cumberland and Westmorland Herald paper he writes for he wrote “As you will be aware, I am no longer allowed to run as Conservative MP in Penrith and The Border.
“Because I have loved the constituency so much, I had considered standing as an Independent; but I have decided that I wouldn’t want to run against those Conservative members who have been such wonderful colleagues over the last 10 years.”