The fact that he did not designate his vice president to take over in his absence has led to fears of a power vacuum and a potential constitutional crisis.
Doctors said in December that President Yar'Adua, 58, was suffering from acute pericarditis, an inflammation of the lining of the heart. He is also known to have kidney problems.
Speaking to the BBC in a three-minute telephone interview organised by the president's office, Mr Yar'Adua said he was making a good recovery.
"At the moment I am undergoing treatment, and I'm getting better from the treatment. I hope that very soon there will be tremendous progress, which will allow me to get back home," he told Mansur Liman from the BBC Hausa service, speaking in both Hausa and English.
BBC Hausa has a large audience in northern Nigeria, where Hausa is the main language.
He said he was in constant contact with Vice-President Goodluck Jonathan, but gave no indication of when he might return to Nigeria.
"I wish, at this stage, to thank all Nigerians for their prayers for my good health, and for their prayers for the nation."
He also wished the Nigerian national football team success in the Africa Cup of Nations currently under way in Angola.
Nigerians fear a political vacuum is developing in the president's absence
The BBC's Will Ross, in Nigeria's capital Abuja, said the president's voice sounded weak.
There is a perceived danger of a power vacuum in a country that only saw the end of military rule just over 10 years ago, our correspondent adds.
But analysts say a handover of power before the next scheduled election in 2011 - to Vice-President Jonathan, a southerner, from President Yar'Adua, a northerner - could disrupt the usual rotation between the regions that has governed Nigeria since the return of civilian rule.
There have also been complaints that important government business has been left hanging in the president's absence.
'We want a telecast'
The interview with President Yar'Adua was recorded late on Monday and first broadcast at 0530 GMT on Tuesday. It has been widely rebroadcast by Nigerian TV and radio stations.
YAR'ADUA ILLNESS TIMELINE
23 November 2009: Goes to hospital in Saudi Arabia
26 November 2009: Presidential doctors say he has pericarditis - inflammation of the heart lining
23 December 2009: First court case filed called him to step down
30 December 2009: Chief justice sworn in. Lawyers say this is illegal in president's absence
5 January 2010: Two more court cases filed and a human rights group wants president declared "missing"
12 January 2010: President gives first interview since going to Saudi Arabia
Many Nigerians will be relieved to hear the president's voice, says our correspondent, but the calls to hand over power to the vice-president will continue.
The National Bar Association and two other groups have launched court cases calling for power to be transferred to Mr Jonathan.
Hundreds of protesters have marched through the streets of Abuja to the national assembly, which was to discuss the president's health on its first day back in session after the Christmas and New Year break.
Nobel laureate Wole Soyinka addressed the rally, saying the president's continued absence - and the lack of an appointed replacement - was allowing corruption to flourish unchecked.
"There is a small cabal which profits by the hiatus in control, in government, in supervision," he said.
"Heaven knows what millions are going down the sink on the lack of supervision."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.