The out-of-contract 32-year-old winger is expected to remain at Hillsborough for a further 12 months.
Johnson broke the news on Twitter by saying: "When I'm back that will get sorted."
Meanwhile Owls chairman Milan Mandaric told the Sheffield Telegraph: "I am very fond of JJ. We are trying to keep him with us; I think he will be okay."
Johnson is currently away on international duty with Jamaica, who face World Cup qualifiers with Mexico, USA and Honduras.
Last season he netted seven times for the South Yorkshire outfit in their first season back in the Championship.