He also praised the Queen’s “dedicated service” during a ceremony that saw the Lord Speaker swear loyalty to the new King.
The monarch was responding to addresses by both Houses of Parliament in Westminster Hall.
King Charles said: “As I stand before you today, I cannot help but feel the weight of history which surrounds us and which reminds us of the vital parliamentary traditions to which members of both Houses dedicate yourselves with such personal commitment, for the betterment of us all.
“Parliament is the living and breathing instrument of our democracy.
“That your traditions are ancient we see in the construction of this great hall and the reminders of mediaeval predecessors of the office to which I have been called and the tangible connections to my darling late mother we see all around us.
“We gather today in remembrance of the remarkable span of the Queen’s dedicated service to her nations and peoples.
“While very young, her late Majesty pledged herself to serve her country and her people and to maintain the precious principles of constitutional government, which lie at the heart of our nation.
“This vow she kept with unsurpassed devotion. She set an example of selfless duty which, with God’s help and your counsels, I am resolved faithfully to follow.”
The King also referenced the connections within Westminster to his mother.
He said: “From the fountain in New Palace Yard, which commemorates the late Queen’s Silver Jubilee, to the sundial in Old Palace Yard for the Golden Jubilee.
“The magnificent stained glass window before me for the Diamond Jubilee.
“And so poignantly, and yet to be formally unveiled, your most generous gift to her late Majesty to mark the unprecedented Platinum Jubilee, which we celebrated only three months ago with such joyful hearts.
“The Great Bell of Big Ben, one of the most powerful symbols of our nation, throughout the world and housed within the Elizabeth Tower, also named for my mother’s Diamond Jubilee, will mark the passage of the late Queen’s progress from Buckingham Palace to this Parliament on Wednesday”.
Lord McFall of Alcluith earlier claimed people would continue to draw strength from the Queen’s “shining example”.
The Lord Speaker said: “In 2012, her late Majesty came to Westminster Hall to mark her Diamond Jubilee and we saw the unveiling of the splendid memorial window, commissioned by both members of Parliament’s Houses, which now graces the north wall of this historic space.
“Like the light that shines through this memorial window, her late Majesty’s magnificent achievements will live on by permanently illuminating and enriching our lives and our national discourse.
“Your Majesty, even as we mourn the loss of our dear Queen, we and future generations will draw strength from her shining example.
“Your Majesty, on behalf of all the members of the House of Lords, I pledge my loyalty to you. I wish you and Her Majesty the Queen Consort well in the life of service to which you have dedicated yourself.
“We are proud and indeed humbled to welcome you as our King. And we look forward to welcoming you on many more occasions to Parliament, and to this hall in the years ahead.”