The commercial public relations executive died on Sunday at the Marymount Hospice in Cork, with Dockery at his bedsid, reported People magazine.
In a statement released through her publicist, Dockery, 34, thanked the public for the "support and kindness" the family has received, before adding that she "kindly request that they are left to grieve in private."
Dineen, from Cork, Ireland, was diagnosed with a rare form of cancer earlier this year.
A senior director at London-based FTI consulting, he is believed to have returned home to Ireland and sought pioneering treatment in Germany following his diagnosis, reports the Irish Independent.