According to The Herald, in a statement sent to through the British Embassy in Harare, Queen Elizabeth II wished Zimbabwe happiness and prosperity.
On the other hand, Obama in his congratulatory message said the US remained committed to the people of Zimbabwe. He said the US would continue to support Zimbabweans as they strived to build a society "that responds to their needs and honours their democratic choices".
The report said Zimbabweans from all walks of life were expected to gather at various centres across the country to commemorate the event.
The main independence celebrations would be in Harare at the National Sports Stadium where President Robert Mugabe will address the nation, the report said.
This year's celebrations will be held under the theme: "Zimbabwe @34: Defending Our Sovereignty and Providing an Enabling Environment for Sustainable Economic Empowerment and Social Transformation."
For many, the celebrations will be overshadowed by the country’s economic meltdown under Mugabe's Zanu PF party.
Economic and political analysts say the former liberation movement has failed to come up with concrete policies to rescue the country from sliding into a full blown economic crisis.