The 24-year-old defender had been without a club after leaving Dagenham & Redbridge earlier this summer.
Hoyte made four senior appearances for Arsenal at the start of his career before leaving the Gunners in 2012.
"I'm pleased to have Gavin on board - he has trained with us for a couple of weeks and has a lot of games under his belt," Gillingham boss Peter Taylor told the club's official site.
"After looking at him we have decided to offer him a contract until the middle of January. I am looking forward to working with him."
Gillingham return to action this evening when they host Swindon Town in League One.