Flags on public buildings were raised at 9am on Wednesday, after the Ministry of Presidential Affairs announced that the 40-day period had drawn to a close on Tuesday night.
“As a nation, we continue to be inspired by the life and example of the late Khalifa bin Zayed,” said Sheikh Mohamed.
He said Sheikh Khalifa, who had led the Emirates since 2004, “will forever remain an enduring symbol of generosity, goodwill and humanitarianism”.
“May his soul rest in peace,” said Sheikh Mohamed in a tribute posted on Twitter on Wednesday evening.
He posted the message alongside a video honouring Sheikh Khalifa.
Sheikh Khalifa died on May 13 at the age of 73.
Work across the country was suspended for three days immediately after his death, flags were lowered to half-staff and life in the UAE took on a more sombre tone.
Sheikh Khalifa was the country's second president after Sheikh Zayed, the Founding Father.
Sheikh Mohamed was elected President by the Federal Supreme Council last month.
Leaders, dignitaries and officials from all over the world travelled to the UAE in the days after Sheikh Khalifa's death to pay tribute to him and to congratulate Sheikh Mohamed on his election.