The 26-year-old, released by the Gills at the end of his contract, becomes United's first signing of the summer after agreeing a two-year deal.
Southend boss Phil Brown told the club website: "I'm delighted to have Myles joining us here at Southend United. His pace and trickery will cause defences in this division all sorts of problems.
"He knows what it takes to win promotion from League Two, having done so with Gillingham a couple of years ago. He's got that experience and should have a big part to play for us next season."