Her commitment to the cause comes after she opened the charity's new building Russell House in Huddersfield in June, which she described as "magical place".
"I was so impressed with the atmosphere you have created at the hospice, and I had a real sense that this was a place of hope in some of the darkest days of a family’s life," she wrote in a letter after visiting.
"I know that you will go from strength to strength and offer support to many more families in West Yorkshire."
The hospice supports more than 50 children and families with life limiting conditions in West Yorkshire.
Peter Branson, the organisation’s chief executive, said, "We are thrilled that Her Royal Highness Princess Beatrice of York has agreed to be our patron.
"Her involvement with our charity will help us to build awareness and to reach out to more families who need our help."
The Princess, 24, who works for a venture capital firm, is already the patron of the York Musical Society and the Helen Arkell Dyslexia centre. The latter helped her manage her dyslexia during her schooling.
The eldest daughter of Prince Andrew and Sarah, Duchess of York opened the hospice's new building in June. She met the children and families that Forget Me Not work with and toured the state of the art facilities.
"It is an incredible honour to be here today to see this dream become a reality," she said.
"With all of your support I know this place can really be the pinnacle of child care, it's a huge honour to be here today."
Beatrice commemorated the opening by unveiling a sculpture donated to the charity by local sculptor Pat Walls.