A statement from the club said the young coach's development over the past 24 months had been "an inspiration to everyone around Cappielow".
Kris Juszczak landed the community coaching job at the club through an employment scheme.
A childrens' holiday camp, which he had been involved with, was cancelled as a mark of respect.
Mr Juszczak had posted a local news article on his Facebook page describing how he landed the job with the club through support from Greenock's Ardgowan Hospice.
He had told how the hospice's Butterfly Project had helped him deal with his grief following the death of his father in 2014.
A support worker had then found him a place on an employment programme.
A Greenock Morton Community football coach has died suddenly at the age of 26.