The 29-year-old right back has been with the Saints since the 2016-17 campaign, helping Brackley become one of the division's top sides.
However, Paul Cox has convinced the former Stamford, Rugby Town and Corby player to seek a fresh challenge at the Jakemans Community Stadium.
Myles was part of the Saints side which finished second last season and conceded just 28 times in 42 matches.
"Ellis has been a consistent performer at this level for a number of years, having experience of numerous play-off campaigns and picking up a winner's medal at Wembley,” manager Paul Cox told bufc.co.uk.
"I feel that he will bring good experience and a knowhow and really compliment his new team-mates."
MORE PILGRIMS: Former players on the move.
MORE PILGRIMS: Midfielder joins from Guiseley.
MORE PILGRIMS: Duxbury departs.