Ameobi signed a short-term contract at Meadow Lane in February 2017 as a free agent.
The striker had been out of the game for nine months following his release by Fleetwood Town.
The former Nigerian international is best known for his time with Newcastle United, where he spent 14 years as a senior professional, playing all but one season in the Premier League.
Home kit: E Sidwell
Away kit: Edward Pearce
Third kit: Gadgy's Drain Services
Boots & socks: Joshua James