Midfielder Heath and striker Griffiths have both featured for the Saddlers' reserve side this term while goalkeeper Roberts has made the bench for manager Dean Smith's first team.
The trio join fellow youth-team players Matt Preston and Reece Flanagan who signed their professional deals earlier this year.
Smith told the club's official website: "The three lads deserve the opportunity to step up and join Matt Preston and Reece Flanagan in getting a professional deal for the new season.
"The hard work is only just beginning for them but I have every faith in them knuckling down and working hard.
"We've had a really strong youth team this year. The players and staff have worked extremely hard."