Midworth, a right-back, was released by the Baggies last week has been training with Hereford.
Bryan Robson made it clear to Midworth that he would be surplus to requirements at the Hawthorns and Midworth and the club decided to part company before the end of the season to help him find a club.
Robson said: "I decided Phil is not part of my plans a few weeks ago but he is a terrific pro who I'm sure will do a good job elsewhere.
Phil hoping to prove his Worth?
Midworth has never played for the Albion first team, and last featured in the 3-3 reserve draw with Newcastle. He is expected to feature in the Reserves' trip to Rochdale on Wednesday.
If the 19-year-old impresses, he could provide cover for Darren Moss, with Town not having a second specialist right-back in their ranks.
If the 19-year-old impresses, he could provide cover for Darren Moss, with Town not having a second specialist right-back in their ranks.