The UAE's Ministry of Presidential Affairs announced Sheikh Khalifa's death on Friday. He was 73.
Oman's period of mourning will last until Sunday.
The Diwan of Oman's Royal Court issued a statement of condolence.
The court said Sheikh Khalifa was among the leaders who “worked to serve [his] Arab and Islamic nation, and led the sisterly United Arab Emirates with determination and perseverance until it became a landmark referred to in all fields”.
Oman News Agency said Sultan Haitham had sent two cables to Sheikh Mohammed bin Rashid, Vice President and Ruler of Dubai, and to Sheikh Mohamed bin Zayed, Crown Prince of Abu Dhabi and Deputy Supreme Commander of the Armed Forces, expressing “sincere condolences and sincere sympathy”.