A plane from Jeddah landed at Abuja airport in the early hours, where an ambulance was waiting on the tarmac.
Earlier this month, Vice-President Goodluck Jonathan became acting leader as fears mounted of a power vacuum.
Mr Yar’Adua has not attended the weekly cabinet meeting, and it is unclear if he is well enough to resume duties.
The 58-year-old leader has been receiving treatment for heart and kidney problems.
An hour after Wednesday’s cabinet meeting was due to begin, ministers were reportedly still waiting inside the presidency, uncertain who was to chair the session.
Acting President Jonathan then postponed it, announcing to ministers that he would hold a special briefing at 1400 (1300 GMT), Reuters news agency reported.
Analysts say there has been considerable jostling for power behind the scenes as politicians look ahead to elections due by April next year.
The BBC’s Ahmed Idris says two planes arrived amid tight security at the presidential wing of Nnamdi Azikiwe International Airport in Abuja at about 0200 local time (0100 GMT).
Although there has been no official confirmation of Mr Yar’Adua’s return, two cabinet ministers told our correspondent the president was on board one of the jets.
And Nigerian Senator Abubakar Umar Gada told the BBC’s World Today: “I can confirm from credible sources the president is back. I think Nigerians will be happy to have their president back in a good shape.”
Presidential adviser Emmanuel Egbogah told Reuters Mr Yar’Adua was back, but it was “doubtful” he would resume office immediately.