Seyed Iman Tabarhosseini, 37, was detained by officers in North London this evening (Monday, April 12), according to Sussex Police.
He remains in police custody and the investigation is continuing, police said.
Police discovered the body of a man in his 50s inside a property in Magdalen Road on Thursday (April 8).
Detective Chief Inspector Emma Vickers said: “This continues to be a fast-moving investigation and we would like to thank the public for their assistance with this matter.
“We continue to appeal to anyone who thinks they might have information to assist our investigation, to come forward to us.
“You can report information to us either online or by calling 101 quoting Operation Leaf.”