Felix, who can also play as a striker, made 32 appearances in all competitions for the National League North club last season, scoring five goals.
The 21-year-old joined Boston in 2014 from Southern Football League Premier Division side St Neots Town.
York were relegated from League Two last season, having won only seven league games.
National League side York City have signed winger Kaine Felix from Boston United on a two-year deal.