Murombedzi made two appearances for Chester and played entirely for free following his January arrival.
The 23-year-old has impressed at wing-back over the last year – having started out his career as an attacking midfielder.
Murombedzi was born in Zimbabwe – and had been at Solihull Moors since the start of the 2016/17 campaign before leaving the club in January.
He spent his younger years at Manchester City and then Reading – before going on to play for Torquay United and Hayes & Yeading United before joining the Moors under current Chester boss Marcus Bignot.
Murombedzi came off the bench in Saturday`s win against the Quakers.