Mekki's ministry was abolished altogether, while Busaidi was replaced by civil service minister Faisal bin Said al-Busaidi, the official ONA news agency said.
The reshuffle had been expected after Sultan Qaboos on Saturday sacked two ministers in response to protesters' grievances, which include corruption and the slow pace of democratic reform.
At least one protester was killed in clashes with police in the northern industrial city of Sohar last week but Oman has been largely spared the violence that has gripped other Arab states including Egypt, Tunisia, Libya and neighbouring Yemen.
A peaceful sit-in at a roundabout in Sohar entered its ninth day Monday with activists demanding the sacking of Mekki and Sultan among others.
One of the protesters, Ali Habib, told AFP the reshuffle was not enough and corrupt ministers needed to face prosecution.
"We want corrupt officials to be brought to justice and put under house arrest," he said.
Demonstrators had "no problems" with Sultan Qaboos himself but intended to escalate their protests with a general strike on Tuesday, he said.
Another crowd has maintained a sit-in outside the seat of the elected consultative council in the capital Muscat, demanding that it be given greater powers.
Washington welcomed the reforms adopted by the authorities in Oman, a key Western ally on the strategic Strait of Hormuz through which 40 percent of the world's oil shipments pass.
"We are encouraged by the recent steps toward reform taken by the government of Oman," State Department spokesman Philip Crowley told reporters.
"And we strongly encourage the government to continue to implement reforms that increase economic opportunity and move toward greater inclusion and participation in the political process."
The sultan earlier announced the creation of 50,000 new jobs and a monthly allowance of 150 riyals ($390, 283 euros) for registered job seekers, and hiked the minimum wage for nationals working in the private sector from $364 to $520.
Thousands have lined up at government offices across Oman to register for jobs with the police and army, as well as in the private sector, an AFP correspondent said.
At a meeting of the six-nation Gulf Cooperation Council, regional foreign ministers expressed strong support for the Omani government.
Oman's top diplomat Yussef bin Alawi told fellow ministers that "change has begun with" the reshuffle and "will continue at the pace in the coming years to make use of the skills of young" Omanis.
He said that the sultanate could start replacing expatriates with Omani workers.
The non-OPEC oil producing nation has a population of around 2.3 million people, of whom 1.96 million are Omani.
It has been ruled by Sultan Qaboos since he overthrew his father, Sultan Said, in a bloodless coup in 1970. The Al-Busaid dynasty has ruled Oman since 1750.