Jenkins - who stepped up from the youth setup at the club - guided the Hoops to a first promotion to Step 1 through the play-offs a year ago.
But after just one season in the National division, the club dropped back into the second tier after finishing 20 points from safety.
The club say his Jenkins' record is 'commendable' despite not being able to beat the drop.
In a statement, the club said: "Ross will always be remembered fondly here as the Manager who helped us reach the highest level we have ever played at.
"To keep us in contention for much of last season, despite the obvious challenges in the higher league, was commendable and it is no surprise that he attracted interest from other clubs: he is a very good coach and I am sure he will go onto have an outstanding career.
"He leaves on very good terms and we have already begun the process of finding his successor.
"The timing allows us to rebuild over the summer and then have a full pre-season to get ready with a new person in charge working towards a new and exciting chapter in our history."