Sheikh Mohamed wished him success in performing his duties as king, following in the footsteps of his mother Queen Elizabeth II.
He expressed his sincere wishes of continued wellness and happiness to the king, and for the further development and prosperity for the UK and its people.
King Charles thanked Sheikh Mohamed for his sincere feelings towards his country and people.
Earlier on Saturday, Sheikh Mohamed spoke to UK Prime Minister Liz Truss, who became the 15th prime minister of the queen's 70-year reign days before the monarch's death.
Queen Elizabeth's 70-year reign - in pictures
He wished Ms Truss success in her appointment and expressed his wishes of continued progress and prosperity for the UK and its people.
He spoke about the deep-rooted historical relations between the UAE and Britain, reaffirming his keenness to develop co-operation for the benefit of the two countries and to support regional and global peace and security.
The UAE enjoyed a warm relationship with Queen Elizabeth, a warmth reflected in its leaders' tributes upon her death on September 8.
President Sheikh Mohamed said on Twitter: “I extend my sincere condolences to the family of Queen Elizabeth II and the people of the UK.
“Her Majesty was a close friend of the UAE and a beloved and respected leader whose long reign was characterised by dignity, compassion and a tireless commitment to serving her country.”
Sheikh Mohammed bin Rashid, Vice President and Ruler of Dubai, who knew the queen for many years, said: “We join the world in mourning the passing of Her Majesty Queen Elizabeth, a global icon who represented the finest qualities of her nation and people.
“Her incredible lifetime of service and duty to the United Kingdom is unparalleled in our modern world.”