The duo won 10 of their 33 matches in charge but only managed two wins in their last 10 in Division One.
The Greenock side ended in eighth place in this season, four points off the relegation play-off zone.
Morton had been in danger of being relegated until the closing stages of the final game of the season.
Grady's side were 1-0 behind to Ayr United before goals in the final 13 minutes by Stewart Greacen and Carlo Monti left Morton's opponents at the bottom of the table.
Airdrie United's defeat by Dunfermline Athletic also meant that Morton escaped a play-off involving the top teams in Division Two.
On Saturday, Airdrie subsequently followed Ayr into the league below after a two-leg play-off semi-final defeat by Brechin City.
Grady was a prolific striker with Clydebank, Dundee, Ayr, Partick Thistle, Dundee United, Gretna and Hamilton Accies before finishing his playing career with Morton.
Source: BBC Sport
Source: BBC Sport