"My priority at this moment is to try and lead the club into League One.
"I have been informed that many Coventry fans voted for me in a local poll and I would like to thank them for their support, but I am sure they can understand the reasons behind my decision.
"Over the past three years, we have worked very hard to get Yeovil Town into this position.
"I feel I have an obligation to the board, the players, the staff and the supporters to complete the job that we have all started here at Huish Park."
Yeovil Chairman John Fry added: "I gave Mike McGinnity a call this morning and informed him of Gary's decision. We are all absolutely delighted and applaud the loyalty that Gary has shown to our club."