She also “fondly” remembered her visit to Ireland a decade ago.
In response Mr Higgins extended his “warmest appreciation for your good wishes on our national day” and described her 2011 visit as a “moment of healing”.
The Queen’s message read: “On the occasion of your National Day, I would like to convey to Your Excellency my congratulations, together with my best wishes to the people of Ireland.
“This year marks ten years since my visit to Ireland, which I remember fondly, and it marks a significant centenary across these islands.
“We share ties of family, friendship and affection – the foundation of our partnership that remains as important today as ten years ago.
She signed off in the Irish language: “La Fheile Padraig sona daoibh go leir.”
Mr Higgins said: “Your special memory of your visit to Ireland ten years ago this year, is one that is shared and invoked regularly by all of us in Ireland, being as it was in its generosity of spirit such a moment of healing.
“It has done so much to deepen our shared sense of the breadth and vibrancy of the connection between our two countries at every level.
“It will continue to inspire the achievement of those possibilities in the future that we might share.”
He said St Patrick’s Day would be celebrated in the hearts of generations of Irish people who have made their home in Britain, and their British friends and family, as well as by the many British people who have happily made their home in Ireland.
“I know that the movement and circulation of our peoples is a source of continuing joy for us both,” he added.
Mr Higgins ended his message in Irish, wishing the Queen and her family a happy and peaceful St Patrick’s Day: “Guim La Fheile Padraig sona agus siochanta ort agus ar do mhuintir”.