Sidibeh arrives at Gorsey Lane following a half-season spell with NWCFL side Cheadle Heath Nomads.
He joined his former club in November 2022, at a time when they were in danger of relegation.
However, a total of 20 goals - including one on his first start for the Nomads against Cheadle Town on Boxing Day last year - saw them climb the table and finish the regular season eighth.
Such form also saw the 25-year-old crowned Cheadle Heath's Players' Player of the Year award, with manager Rory Fallon stating at the time that the former AFC Blackpool striker had a "bright future ahead of him".
Sidibeh made his Rylands debut on Saturday, scoring the only goal of the game as they beat West Didsbury and Chorlton 1-0 in a pre-season friendly.
He becomes the Blues' latest new recruit as they prepare for their first full season under the guidance of Michael Clegg, who was appointed to the role in February.