About 15,000 signed a petition this year over the issue.
Healthcare campaigner Gill George, from Shropshire Defend Our NHS, said: “Almost all local people will have used Shropdoc’s services either for themselves, for a family member, a child, a parent, a partner and Shropdoc works.
“Shropdoc delivers and people are really, really scared by the prospect of losing that.”
HealthHero said its “proven and effective model” had delivered high-quality out-of-hours care for more than 20 years, and was twice rated outstanding by the Care Quality Commission.
Dr Sue Lavelle, HealthHero medical director, said “local bases will remain in place, services will continue to be delivered by local clinicians, and palliative and end-of-life care will be maintained”.