Cox, who signed for the League Two club this week following his release by Leyton Orient, is unable to play for the Reds until January 2 2017 but is able to sign for clubs below National League level.
The 29-year-old left the O's at the beginning of the month after six years at Brisbane Road, in which he scored 59 goals in 275 appearances.
The Hillians announced on Friday that Cox would be linking up with manager Ian Chapman, his former Brighton & Hove Albion coach.
After being reunited until the end of the year, pictured, a delighted Chapman told Hillians fans: “This is a great signing for the club and I am looking forward to working with Dean again. He will add quality to the squad who have started the season well.
"We have games coming up ‘thick and fast’ and Dean can play a vital part in us gaining points in the Ryman's Premier League."
Crawley`s head coach Dermot Drummy said: “It was always our intention to get Dean out on loan to a local club so he could get some games under his belt and keep himself ticking over before he can play for us. Burgess Hill is not only local to him geographically, but he knows Ian Chapman well and we know Burgess Hill are an excellent club who try and play in the right way."
He added: “It’s an arrangement which suits everyone. Dean will train with us during the week and also play for Burgess Hill and we’ll obviously be monitoring his progress.”
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