McGuinness will be assisted by his father Laurie McGuinness, who succeeds Mark Roberts.
Rhyl parted company with Owen and Roberts in a bid to avoid relegation from the Welsh Premier League.
They are second from bottom of the table with only three wins from 24 games this season.
Only last season's promoted team Haverfordwest are below Rhyl, who have not won since October, 2015.
Since then they have not won in 12 league games.
Rhyl stated "disappointing results" led to the departures of Owen and Roberts.
Rhyl FC have promoted Niall McGuinness from academy director to manager their first team after parting company with Gareth Owen.